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Actor-critic (AC) cooperative multiagent reinforcement learning (MARL) over directed graphs is studied in this article. The goal of the agents in MARL is to maximize the globally averaged return in a distributed way, i.e., each agent can only exchange information with its neighboring agents. AC methods proposed in the literature require the communication graphs to be undirected and the weight matrices to be doubly stochastic (more precisely, the weight matrices are row stochastic and their expectation are column stochastic). Differently from these methods, we propose a distributed AC algorithm for MARL over directed graph with fixed topology that only requires the weight matrix to be row stochastic. Then, we also study the MARL over directed graphs (possibly not connected) with changing topologies, proposing a different distributed AC algorithm based on the push-sum protocol that only requires the weight matrices to be column stochastic. Convergence of the proposed algorithms is proven for linear function approximation of the action value function. Simulations are presented to demonstrate the effectiveness of the proposed algorithms., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Bart De Schutter

The current synthetic-aperture-radar (SAR) image formation algorithms have been developed for the pulse radar systems, and they are desired to be used for frequency modulated continuous wave (FMCW) radar systems. Since there is a difference between the outputs of pulse radar and FMCW radar, it is necessary to adapt these algorithms to the output of the pulse radar. Beside this, the start-stop approximation, which can be used for signal processing of pulse radar systems, should be taken into account for FMCW radar systems due to the fact that the pulse duration of pulse radar is relatively small in comparison to the modulation time of FMCW radar. The study investigates the phase error caused by the start-stop approximation in processing the data measured by a FMCW radar system for synthetic aperture imaging. The important finding is that the start-stop approximation is valid for processing FMCW SAR data in many cases. If the following circumstances occur simultaneously, such as high radar signal frequency, long modulation time, high platform speed, and short propagation range, then the approximation may become invalid. The simulations and the experiments performed with a wideband 154 GHz FMCW radar support this statement. Author, Project Multistatic High-Resolution Sensing at THz

The current synthetic-aperture-radar (SAR) image formation algorithms have been developed for the pulse radar systems, and they are desired to be used for frequency modulated continuous wave (FMCW) radar systems. Since there is a difference between the outputs of pulse radar and FMCW radar, it is necessary to adapt these algorithms to the output of the pulse radar. Beside this, the start-stop approximation, which can be used for signal processing of pulse radar systems, should be taken into account for FMCW radar systems due to the fact that the pulse duration of pulse radar is relatively small in comparison to the modulation time of FMCW radar. The study investigates the phase error caused by the start-stop approximation in processing the data measured by a FMCW radar system for synthetic aperture imaging. The important finding is that the start-stop approximation is valid for processing FMCW SAR data in many cases. If the following circumstances occur simultaneously, such as high radar signal frequency, long modulation time, high platform speed, and short propagation range, then the approximation may become invalid. The simulations and the experiments performed with a wideband 154 GHz FMCW radar support this statement. Author, Project Multistatic High-Resolution Sensing at THz

The current synthetic-aperture-radar (SAR) image formation algorithms have been developed for the pulse radar systems, and they are desired to be used for frequency modulated continuous wave (FMCW) radar systems. Since there is a difference between the outputs of pulse radar and FMCW radar, it is necessary to adapt these algorithms to the output of the pulse radar. Beside this, the start-stop approximation, which can be used for signal processing of pulse radar systems, should be taken into account for FMCW radar systems due to the fact that the pulse duration of pulse radar is relatively small in comparison to the modulation time of FMCW radar. The study investigates the phase error caused by the start-stop approximation in processing the data measured by a FMCW radar system for synthetic aperture imaging. The important finding is that the start-stop approximation is valid for processing FMCW SAR data in many cases. If the following circumstances occur simultaneously, such as high radar signal frequency, long modulation time, high platform speed, and short propagation range, then the approximation may become invalid. The simulations and the experiments performed with a wideband 154 GHz FMCW radar support this statement. Author, Project Multistatic High-Resolution Sensing at THz

The current synthetic-aperture-radar (SAR) image formation algorithms have been developed for the pulse radar systems, and they are desired to be used for frequency modulated continuous wave (FMCW) radar systems. Since there is a difference between the outputs of pulse radar and FMCW radar, it is necessary to adapt these algorithms to the output of the pulse radar. Beside this, the start-stop approximation, which can be used for signal processing of pulse radar systems, should be taken into account for FMCW radar systems due to the fact that the pulse duration of pulse radar is relatively small in comparison to the modulation time of FMCW radar. The study investigates the phase error caused by the start-stop approximation in processing the data measured by a FMCW radar system for synthetic aperture imaging. The important finding is that the start-stop approximation is valid for processing FMCW SAR data in many cases. If the following circumstances occur simultaneously, such as high radar signal frequency, long modulation time, high platform speed, and short propagation range, then the approximation may become invalid. The simulations and the experiments performed with a wideband 154 GHz FMCW radar support this statement. Author, Project Multistatic High-Resolution Sensing at THz

Age of Information, which emerged as a new metric to quantify the freshness of information, has attracted increasing interests recently. To optimize the system AoI, most existing works try to compute an efficient schedule from the point of data transmission. Unfortunately, at wireless-powered network edge, the charging schedule of the source nodes also needs to be decided besides data transmission. Thus, in this paper, we investigate the joint scheduling problem of data transmission and energy replenishment to optimize the maximum peak AoI at network edge with directional chargers. To the best of our knowledge, this is the first work that considers such two problems simultaneously. Firstly, the theoretical bounds of the maximum peak AoI with respect to the charging latency are derived. Secondly, for the minimum peak AoI scheduling problem with a single charger, an optimal scheduling algorithm is proposed to minimize the charging latency, and then a data transmission scheduling strategy is also given to optimize the maximum peak AoI. The proposed algorithm is proved to have a constant approximation ratio of up to 1.5. As for the scenario with multiple chargers, an approximate algorithm is also proposed to minimize the charging latency and the maximum peak AoI. Additionally, when the network bandwidth constraint is considered, the algorithm which considers the parallelism of the charging process and data transmission process is also proposed to reduce the latency and the maximum peak AoI. Finally, the theoretical analysis and simulation results verify that the proposed algorithms have high performance in terms of latency and AoI. IEEE

As one of the core technologies for 5G systems, massive multiple-input multiple-output (MIMO) introduces dramatic capacity improvements along with very high beamforming and spatial multiplexing gains. When developing efficient physical layer algorithms for massive MIMO systems, message passing is one promising candidate owing to its superior performance. However, as their computational complexity increases dramatically with the problem size, the state-of-the-art message passing algorithms cannot be directly applied to future 6G systems, where an exceedingly large number of antennas are expected to be deployed. To address this issue, we propose a model-driven deep learning (DL) framework, namely the AMP-GNN for massive MIMO transceiver design, by considering the low complexity of the AMP algorithm and adaptability of GNNs. Specifically, the structure of the AMP-GNN network is customized by unfolding the approximate message passing (AMP) algorithm and introducing a graph neural network (GNN) module into it. The permutation equivariance property of AMP-GNN is proved, which enables the AMP-GNN to learn more efficiently and to adapt to different numbers of users. We also reveal the underlying reason why GNNs improve the AMP algorithm from the perspective of expectation propagation, which motivates us to amalgamate various GNNs with different message passing algorithms. In the simulation, we take the massive MIMO detection to exemplify that the proposed AMP-GNN significantly improves the performance of the AMP detector, achieves comparable performance as the state-of-the-art DL-based MIMO detectors, and presents strong robustness to various mismatches. IEEE

The mean and variance of portfolio returns are the standard quantities to measure the expected return and risk of a portfolio. Efficient portfolios that provide optimal trade-offs between mean and variance warrant consideration. To express a preference among these efficient portfolios, investors have put forward many mean-variance portfolio (MVP) formulations which date back to the classical Markowitz portfolio. However, most existing algorithms are highly specialized to particular formulations and cannot be generalized for broader applications. Therefore, a fast and unified algorithm would be extremely beneficial. In this paper, we first introduce a general MVP problem formulation that can fit most existing cases by exploring their commonalities. Then, we propose a widely applicable and provably convergent successive quadratic programming algorithm (SCQP) for the general formulation. The proposed algorithm can be implemented based on only the QP solvers and thus is computationally efficient. In addition, a fast implementation is considered to accelerate the algorithm. The numerical results show that our proposed algorithm significantly outperforms the state-of-the-art ones in terms of convergence speed and scalability.

Massive access has been challenging for the fifth generation (5 G) and beyond since the abundance of devices causes communication overload to skyrocket. In an uplink massive access scenario, device traffic is sporadic in any given coherence time. Thus, channels across the antennas of each device exhibit correlation, which can be characterized by the row sparse channel matrix structure. In this work, we develop a bilinear generalized approximate message passing (BiGAMP) algorithm based on the row sparse channel matrix structure. This algorithm can jointly detect device activities, estimate channels, and detect signals in massive multiple-input multiple-output (MIMO) systems by alternating updates between channel matrices and signal matrices. The signal observation provides additional information for performance improvement compared to the existing algorithms. We further analyze state evolution (SE) to measure the performance of the proposed algorithm and characterize the convergence condition for SE. Moreover, we perform theoretical analysis on the error probability of device activity detection, the mean square error of channel estimation, and the symbol error rate of signal detection. The numerical results demonstrate the superiority of the proposed algorithm over the state-of-the-art methods in DAD-CE-SD, and the numerical results are relatively close to the theoretical analysis results.

In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. We first develop a general algorithmic framework, in which each node constructs a local, inexact quasi-Newton direction that asymptotically approaches the global, exact one at each time step. To do so, a local gradient approximation is constructed using dynamic average consensus to track the average of variance-reduced local stochastic gradients over the entire network, followed by a proper local Hessian inverse approximation. We show that under standard convexity and smoothness assumptions on the cost functions, the methods obtained from our framework converge linearly to the optimal solution if the local Hessian inverse approximations used have uniformly bounded positive eigenvalues. To construct the Hessian inverse approximations with the said boundedness property, we design two fully decentralized stochastic quasi-Newton methods-namely, the damped regularized limited-memory DFP (Davidon-Fletcher-Powell) and the damped limited-memory BFGS (Broyden-Fletcher-Goldfarb-Shanno)-which use a fixed moving window of past local gradient approximations and local decision variables to adaptively construct Hessian inverse approximations. A noteworthy feature of these methods is that they do not require extra sampling or communication. Numerical results show that the proposed decentralized stochastic quasi-Newton methods are much faster than the existing decentralized stochastic first-order algorithms., QC 20230403

In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several variants of this problem that are known to be N P-hard, while also proving N P-hardness for two variants whose complexity was unknown before. Using these results, together with constant-factor approximations for the makespan objective from the literature, we also introduce the first results on bi-objective approximation in the coupled task setting.

In the general max-min fair allocation problem, there are m players and n indivisible resources, each player has his/her own utilities for the resources, and the goal is to find an assignment that maximizes the minimum total utility of resources assigned to a player. The problem finds many natural applications such as bandwidth distribution in telecom networks, processor allocation in computational grids, and even public-sector decision making. We introduce an over-estimation strategy to design approximation algorithms for this problem. When all utilities are positive, we obtain an approximation ratio of c /1-C , where c is the maximum ratio of the largest utility to the smallest utility of any resource. When some utilities are zero, we obtain an approximation ratio of (1 + 3 c((sic) )+ O(delta c((sic)2))), where c circumflex expressionccent is the maximum ratio of the largest utility to the smallest positive utility of any resource.

We consider the watchman route problem for a k-transmitter watchman: standing at point p in a polygon P, the watchman can see if intersects P’s boundary at most k times—q is k-visible to p. Traveling along the k-transmitter watchman route, either all points in P or a discrete set of points must be k-visible to the watchman. We aim for minimizing the length of the k-transmitter watchman route. We show that even in simple polygons the shortest k-transmitter watchman route problem for a discrete set of points is NP-complete and cannot be approximated to within a logarithmic factor (unless P=NP), both with and without a given starting point. Moreover, we present a polylogarithmic approximation for the k-transmitter watchman route problem for a given starting point and with approximation ratio (with)., Funding agencies: Supported by grants 2018-04001 (Nya paradigmer för autonom obemannad flygledning) and 2021-03810 (Illuminate: bevisbart goda algoritmer för bevakningsproblem) from the Swedish Research Council (Vetenskapsrådet).

Exploration efficiency of GAs largely depends on parameter values. But, it is hard to manually adjust these values. To cope with this problem, several adaptive GAs which automatically adjust parameters have been proposed. However, most of the existing adaptive GAs can adapt only a few parameters at the same time. Although several adaptive GAs can adapt multiple parameters simultaneously, these algorithms require extremely large computation costs. In this paper, we propose self adaptive island GA (SAIGA) which adapts four parameter values simultaneously while finding a solution to a problem. SAIGA is a kind of island GA, and it adapts parameter values using a similar mechanism to meta-GA. Throughout our evaluation experiments, we confirmed that our algorithm outperforms a simple GA using De Jong's rational parameters, and has performance close to a simple GA using manually tuned parameter values., CEC '03 : IEEE Congress on Evolutionary Computation , Dec 8-12, 2003 , Canberra, Australia

Online Event-based social networks (EBSNs), such as Meetup and Whova, which provide platforms for users to publish, arrange and participate in events, have become increasingly popular. A major challenge for managing EBSNs is to generate the most satisfactory event arrangement, i.e., events are scheduled at the reasonable time to attract maximum number of participants. Existing approaches usually focus on assigning a set of events organized to time intervals, but ignore the competitive relationships among different event organizers, which will lead to event time allocations unacceptable to organizers. Thus, a more intelligent EBSNs platform that allocates social events properly in a global view (i.e., the perspective of platform) is desired. In this paper, we first formally define the problem of Platform-oriented Event Time Allocation (PETA), which contains two parts: the prediction of event feasible time period and the event time allocation. Unfortunately, we find that the PETA problem is NP-hard due to the global conflict constraints on events. Thus, we propose a method to calculate event feasible time period based on event time prediction, and then design a greedy algorithm and two approximation algorithms to solve the PETA problem. Finally, we conduct extensive experiments on both real and synthetic datasets to test the effectiveness and efficiency of the proposed algorithms. © 1989-2012 IEEE.

In the area of autonomous driving, it typically brings great difficulty in solving the motion planning problem since the vehicle model is nonlinear and the driving scenarios are complex. Particularly, most of the existing methods cannot be generalized to dynamically changing scenarios with varying surrounding vehicles. To address this problem, this development here investigates the framework of integrated decision and control. As part of the modules, static path planning determines the reference candidates ahead, and then the optimal path-tracking controller realizes the specific autonomous driving task. An innovative and effective constrained finite-horizon approximate dynamic programming (ADP) algorithm is herein presented to generate the desired control policy for effective path tracking. With the generalized policy neural network that maps from the state to the control input, the proposed algorithm preserves the high effectiveness for the motion planning problem towards changing driving environments with varying surrounding vehicles. Moreover, the algorithm attains the noteworthy advantage of alleviating the typically heavy computational loads with the mode of offline training and online execution. As a result of the utilization of multi-layer neural networks in conjunction with the actor-critic framework, the constrained ADP method is capable of handling complex and multidimensional scenarios. Finally, various simulations have been carried out to show that the constrained ADP algorithm is effective. IEEE

The minimum vertex cover problem (MinVertexCover) is an important optimization problem in graph theory, with applications in numerous fields outside of mathematics. As MinVertexCover is an NP-hard problem, there currently exists no efficient algorithm to find an optimal solution on arbitrary graphs. We consider quantum optimization algorithms, such as the Quantum Alternating Operator Ansatz (QAOA+), to find good minimum vertex covers. This thesis presents new 'second degree' mixing Hamiltonians for MinVertexCover in the QAOA+ framework, which allow mixing between solutions Hamming distance 2 apart. The performance of these new Hamiltonians is evaluated on a small graph. Methods to extend this idea by constructing Hamiltonians which allow mixing between solutions at Hamming distance n are also presented, along with a generalization of second degree mixing Hamiltonians to other optimization problems., Applied Mathematics

Range aggregation is a primitive operation in spatial data applications and there is a growing demand to support such operations over a data federation, where the entire spatial data are separately held by multiple data providers (a.k.a., data silos). Data federations notably increase the amount of data available for data-intensive applications such as smart mobility planning and public health emergency responses. Yet they also challenge the conventional implementation of range aggregation queries because the raw data cannot be shared within the federation and the data partition at each data silo is fixed during query processing. These constraints limit the design space of distributed range aggregation query processing. In this work, we propose approximate algorithms for efficient range aggregation over spatial data federation. We devise novel single-silo sampling algorithms that process queries in parallel and design a level sampling based algorithm which reduces the time complexity of local queries at each data silo to O(log 1/), where is the approximation ratio of the accuracy guarantee. Extensive evaluations with real-world data show that compared with state-of-the-arts, our solutions reduce the time cost and communication cost by up to 85.1x and 5.5x respectively, with average approximate errors of below 2.8%. IEEE

This paper investigates a multi-user wireless powered fog computing (FC) network, where energy-limited wireless sensor devices (WSDs) first harvest energy from a nearby hybrid access point (HAP) and then, compute their tasks locally (i.e., the local computing (LC) mode) or offload the tasks to the HAP (i.e., the FC mode) via a binary offloading policy. An optimization problem is formulated to minimize the transmit power at the HAP by jointly optimizing the time allocation ratio and the computing mode selection vector, under the energy causality constraints and the WSDs computing rate requirements constraints. To efficiently solve the formulated non-convex problem in a distributed manner, an alternating direction method of multipliers (ADMM)-based algorithm is designed. With our presented ADMM-based algorithm, each WSD is able to optimize its computing mode and offloading time with local channel state information (CSI). For comparison, a channel-sorting-based (CSB) centralized algorithm with global CSI is also designed. Simulation results show that the proposed distributed algorithm achieves the comparable performance with the centralized algorithm or by using the exhaustive search one. Moreover, to minimize the transmit power, the WSDs with the better channel quality are inclined to select the LC mode, which is much different from traditional design.

Mobile Edge Computing (MEC) has been identified as a desirable computing paradigm that provides efficient and effective services for various applications, while meeting stringent service delay requirements. Orthogonal to the MEC computing paradigm, Network Function Virtualization (NFV) technology is another enabling technology that provides the network resource management with great flexibility and scalability, where the instances of Virtual Network Functions (VNFs) are deployed in edge servers as Service Function Chains (SFCs) for SFC-enabled services. Although reliable service provisioning in MEC environments is fundamentally important, the deployed VNF instances usually are not reliable, which can be affected by their software implementation, their execution duration, the workload among edge servers, and so on. Empowered by digital twin techniques, the states of VNF instances can be maintained by their digital twins in a real-time manner and their reliability can be accurately predicted through their digital twins. In this paper, we study digital twin-assisted, SFC-enabled reliable service provisioning in MEC networks by exploiting the dynamics of VNF instance reliability. We concentrate on two novel optimization problems of reliable service provisioning: the service cost minimization problem, and the dynamic service admission maximization problem. We first show their NP-hardness. We then formulate an Integer Linear Program (ILP) solution, and devise an approximation algorithm with a constant approximation ratio for the service cost minimization problem. We thirdly provide an ILP solution to the offline version of the dynamic service admission maximization problem. Built upon this offline ILP solution, we also develop an online algorithm with a provable competitive ratio for the problem, by adopting the primal-dual dynamic updating technique. We finally evaluate the performance of the proposed algorithms via simulations. Simulation results demonstrate that the pr

Mobile Edge Computing (MEC) promises to provide mobile users with delay-sensitive services at the edge of network, and each user service request usually is associated with a Service Function Chain (SFC) requirement that consists of Virtualized Network Functions (VNFs) in order. The satisfaction of a user on his requested service is heavily impacted by the service reliability. In this paper, we study user satisfaction on services provided by an MEC network through introducing a submodular function based metric to measure user satisfaction. We first formulate a novel user satisfaction problem with the aim to maximize the accumulative user satisfaction, assuming that all available computing resource in the MEC network can be used for service reliability enhancement. We show that the problem is NP-hard, and devise an approximation algorithm with a provable approximation ratio for it. We then consider the problem under a given computing resource budget constraint, for which we devise an approximation algorithm with a provable approximation ratio, at the expense of moderate budget violations. We finally evaluate the performance of the proposed algorithms through experimental simulations. Simulation results demonstrate that the proposed algorithms outperform the comparison baseline algorithms, improving the performance by more in comparison with the baseline algorithms. IEEE

We formulate the optimal flow problem in a multi-area integrated electrical and gas system as a mixed-integer optimization problem by approximating the non-linear gas flows with piece-wise affine functions, thus resulting in a set of mixed-integer linear constraints. For its solution, we propose a novel algorithm that consists in one stage for solving a convexified problem and a second stage for recovering a mixed-integer solution. The latter exploits the gas flow model and requires solving a linear program. We provide an optimality certificate for the computed solution and show the advantages of our algorithm with respect to the state-of-the-art method via numerical simulations., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Sergio Grammatico, Team Bart De Schutter

This paper studies how to estimate the weighted adjacency matrix of a network out of the state sequence of a model with binary-valued states, by using a recursive algorithm. In the considered system, agents display and exchange these binary-valued states generated from intrinsic quantizers. It is shown that stability of the model and identifiability of the system parameters can be guaranteed under continuous random noise. Under standard Gaussian noise, the problem of estimating the real-valued weighted adjacency matrix and the unknown quantization threshold is transformed to an optimization problem via a maximum likelihood approach. It is further verified that the unique solution of the optimization problem is the true parameter vector. A recursive algorithm for the estimation problem is then proposed based on stochastic approximation techniques. Its strong consistency is established and convergence rate analyzed. Numerical simulations are provided to illustrate developed results., QC 20230510

This paper investigates solving convex composite optimization on an undirected network, where each node, privately endowed with a smooth component function and a nonsmooth one, is required to minimize the sum of all the component functions throughout the network. To address such a problem, a general Approximate Method of Multipliers (AMM) is developed, which attempts to approximate the Method of Multipliers by virtue of a surrogate function with numerous options. We then design the possibly nonseparable, time-varying surrogate function in various ways, leading to different distributed realizations of AMM. We demonstrate that AMM generalizes more than ten state-of-the-art distributed optimization algorithms, and certain specific designs of its surrogate function result in a variety of new algorithms to the literature. Furthermore, we show that AMM is able to achieve an $O(1/k)$ rate of convergence to optimality, and the convergence rate becomes linear when the problem is locally restricted strongly convex and smooth. Such convergence rates provide new or stronger convergence results to many prior methods that can be viewed as specializations of AMM., QC 20230508

We study the Minimum Sum Vertex Cover problem, which asks for an ordering of vertices in agraph that minimizes the total cover time of edges. In particular, n vertices of the graph are visitedaccording to an ordering, and for each edge this induces the first time it is covered. The goal of theproblem is to find the ordering which minimizes the sum of the cover times over all edges in thegraph.In this work we give the first explicit hardness of approximation result for Minimum Sum VertexCover. In particular, assuming the Unique Games Conjecture, we show that the Minimum SumVertex Cover problem cannot be approximated within 1.014. The best approximation ratio forMinimum Sum Vertex Cover as of now is 16/9, due to a recent work of Bansal, Batra, Farhadi, andTetali.We also revisit an approximation algorithm for regular graphs outlined in the work of Feige,Lovász, and Tetali, and show that Minimum Sum Vertex Cover can be approximated within 1.225on regular graphs, QC 20230508

In recent years we have witnessed an increase on the development of methods for submodular optimization, which have been motivated by the wide applicability of submodular functions in real-world data-science problems. In this paper, we contribute to this line of work by considering the problem of robust submodular maximization against unexpected deletions, which may occur due to privacy issues or user preferences. Specifically, we consider the minimum number of items an algorithm has to remember, in order to achieve a non-trivial approximation guarantee against adversarial deletion of up to d items. We refer to the set of items that an algorithm has to keep before adversarial deletions as a deletion-robust coreset. Our theoretical contributions are two-fold. First, we propose a single-pass streaming algorithm that yields a (1 - 2 is an element of)/(4p)approximation for maximizing a non-decreasing submodular function under a general p-matroid constraint and requires a coreset of size k+ d/is an element of, where k is the maximum size of a feasible solution. To the best of our knowledge, this is the first work to achieve an (asymptotically) optimal coreset, as no constant-factor approximation is possible with a coreset of size sublinear in d. Second, we devise an effective offline algorithm that guarantees stronger approximation ratios with a coreset of size O( d log(k)/is an element of). We also demonstrate the superior empirical performance of the proposed algorithms in real-life applications., QC 20230523

We consider the problem of adding a fixed number of new edges to an undirected graph in order to minimize the diameter of the augmented graph, and under the constraint that the number of edges added for each vertex is bounded by an integer. The problem is motivated by network-design applications, where we want to minimize the worst case communication in the network without excessively increasing the degree of any single vertex, so as to avoid additional overload. We present three algorithms for this task, each with their own merits. The special case of a matching augmentation -when every vertex can be incident to at most one new edge- is of particular interest, for which we show an inapproximability result, and provide bounds on the smallest achievable diameter when these edges are added to a path. Finally, we empirically evaluate and compare our algorithms on several real-life networks of varying types., QC 20230522

The WMMSE beamforming algorithm is a popular approach to address the NP-hard weighted sum rate (WSR) maximization beamforming problem. Although it efficiently finds a local optimum, it requires matrix inverses, eigendecompositions, and bisection searches, operations that are problematic for real-time implementation. In our previous work, we considered the MU-MISO case with single-antenna receivers and effectively replaced such operations by resorting to a first-order method. Here, we consider the more general and challenging MU-MIMO case with multiple-antenna receivers. Our earlier approach does not generalize to this scenario and cannot be applied to replace all the hard-to-parallelize operations that appear in the MU-MIMO case. Thus, we propose to leverage a reformulation of the auxiliary WMMSE function given by Hu et al. By applying gradient descent and Schulz iterations, we formulate the first variant of the WMMSE algorithm applicable to the MU-MIMO case that is free from matrix inverses and other serial operations and hence amenable to both real-time implementation and deep unfolding. From a theoretical viewpoint, we establish its convergence to a stationary point of the WSR maximization problem. From a practical viewpoint, we show that in a deep-unfolding-based implementation, the matrix-inverse-free WMMSE algorithm attains, within a fixed number of iterations, a WSR comparable to the original WMMSE algorithm truncated to the same number of iterations, yet with significant implementation advantages in terms of parallelizability and real-time execution., QC 20230320

In this work, we extend the regularization framework from Kronqvist et al. (Math Program 180(1):285–310, 2020) by incorporating several new regularization functions and develop a regularized single-tree search method for solving convex mixed-integer nonlinear programming (MINLP) problems. We propose a set of regularization functions based on distance metrics and Lagrangean approximations, used in the projection problem for finding new integer combinations to be used within the Outer-Approximation (OA) method. The new approach, called Regularized Outer-Approximation (ROA), has been implemented as part of the open-source Mixed-integer nonlinear decomposition toolbox for Pyomo—MindtPy. We compare the OA method with seven regularization function alternatives for ROA. Moreover, we extend the LP/NLP Branch and Bound method proposed by Quesada and Grossmann (Comput Chem Eng 16(10–11):937–947, 1992) to include regularization in an algorithm denoted RLP/NLP. We provide convergence guarantees for both ROA and RLP/NLP. Finally, we perform an extensive computational experiment considering all convex MINLP problems in the benchmark library MINLPLib. The computational results show clear advantages of using regularization combined with the OA method., QC 20230404

We present a new mixed integer formulation for the discrete informative path planning problem in random fields. The objective is to compute a budget constrained path while collecting measurements whose linear estimate results in minimum error over a finite set of prediction locations. The problem is known to be NP-hard. However, we strive to compute optimal solutions by leveraging advances in mixed integer optimization. Our approach is based on expanding the search space so we optimize not only over the collected measurement subset, but also over the class of all linear estimators. This allows us to formulate a mixed integer quadratic program that is convex in the continuous variables. The formulations are general and are not restricted to any covariance structure of the field. In simulations, we demonstrate the effectiveness of our approach over previous branch and bound algorithms., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Learning & Autonomous Control

As a crucial and widely researched application in social networks, social advertising refers to selecting seed users for several advertisers to propagate their advertisements in the network via a information cascade effect. Prior studies on this topic have presented approximation algorithms merely for maximizing the expected revenue. However, regarding to the fairness issue, no existing works have provided effective solution. Such a issue would cause polarized revenues among different advertisers and the draining of them. In this paper, we investigate the fairness issue in social advertising. That is, how the social network platform owner distributes seeds users fairly to different advertisers. We define the fairness metric according to the maximin share, a concept about fair distribution in computation economics, and develop a novel approximation algorithm. Our approach achieves an approximation factor of (1-1/e)2/3 1/h2, where h is the number of different advertisers. Our result recovers the best-known proposed (1-1/e)2/2. -approximation ratio when h=1 and extends settings to a more general case. The evaluation on real datasets indicates that our solution is effective and outperforms the existing algorithms in terms of fairness. © 2022 IEEE.

The Hamilton-Jacobi-Bellman (HJB) equation serves as the necessary and sufficient condition for the optimal solution to the continuous-time (CT) optimal control problem (OCP). Compared with the infinite-horizon HJB equation, the solving of the finite-horizon (FH) HJB equation has been a long-standing challenge, because the partial time derivative of the value function is involved as an additional unknown term. To address this problem, this study first-time bridges the link between the partial time derivative and the terminal-time utility function, and thus it facilitates the use of the policy iteration (PI) technique to solve the CT FH OCPs. Based on this key finding, the FH approximate dynamic programming (ADP) algorithm is proposed leveraging an actor-critic framework. It is shown that the algorithm exhibits important properties in terms of convergence and optimality. Rather importantly, with the use of multilayer neural networks (NNs) in the actor-critic architecture, the algorithm is suitable for CT FH OCPs toward more general nonlinear and complex systems. Finally, the effectiveness of the proposed algorithm is demonstrated by conducting a series of simulations on both a linear quadratic regulator (LQR) problem and a nonlinear vehicle tracking problem.

Current trends in power system development and the issues they pose have increased the urgency of automatic and emergency control alongside transient electromechanical processes. Such control devices place high demands on mode-parameter estimation algorithms in terms of their speed, accuracy, and transient sensitivity. This paper proposes a rapid estimation algorithm for power system parameters to investigate its optimal settings and applicability in both static and dynamic states. The proposed algorithm is based on signal approximation on sliding window using a multiparameter model, which is highly stable and reliable. The signals modeled in MATLAB/Simulink were used as initial data. From the experimental results, it became clear that the rapid estimation algorithm of the power system parameters showed high accuracy in steady-state mode as well as during transients, and its optimal parameters were identified. The developed algorithm can be used in relay protection, automatic and emergency control devices, and synchronous machine state-monitoring systems. © 2013 IEEE.

A quantitative description of the excited electronic states of point defects and impurities is crucial for understanding materials properties, and possible applications of defects in quantum technologies. This is a considerable challenge for computational methods, since Kohn-Sham density functional theory (DFT) is inherently a ground-state theory, while higher-level methods are often too computationally expensive for defect systems. Recently, embedding approaches have been applied that treat defect states with many-body methods, while using DFT to describe the bulk host material. We implement such an embedding method, based on Wannierization of defect orbitals and the constrained random-phase approximation approach, and perform systematic characterization of the method for three distinct systems with current technological relevance: a carbon dimer replacing a B and N pair in bulk hexagonal BN (CBCN), the negatively charged nitrogen-vacancy center in diamond (NV-), and an Fe impurity on the Al site in wurtzite AlN (FeAl). In the context of these test-case defects, we demonstrate that crucial considerations of the methodology include convergence of the bulk screening of the active-space Coulomb interaction, the choice of exchange-correlation functional for the initial DFT calculation, and the treatment of the "double-counting"correction. For CBCN we show that the embedding approach gives many-body states in agreement with analytical results on the Hubbard dimer model, which allows us to elucidate the effects of the DFT functional and double-counting correction. For the NV- center, our method demonstrates good quantitative agreement with experiments for the zero-phonon line of the triplet-triplet transition. Finally, we illustrate challenges associated with this method for determining the energies and orderings of the complex spin multiplets in FeAl. © 2022 American Physical Society.

With the emergence of energy communities, where a number of prosumers (consumers with their own energy generation) invest in shared renewable generation capacity and battery storage, the issue of fair allocation of benefits and costs has become increasingly important. The Shapley value, a solution concept in cooperative game theory initially proposed by Nobel prize-winning economist Lloyd Shapley, has attracted increasing interest for redistribution in energy settings. However, due to its high time complexity, it is intractable beyond communities of a few dozen prosumers. This study proposes a new deterministic method for approximating the Shapley value in realistic community energy settings and compares its performance with existing methods. To provide a benchmark for the comparisons of these methods, we also design a novel method to compute the exact Shapley value for communities of up to several hundred agents by clustering consumers into a smaller number of demand profiles. Experimental analyses with large-scale case studies of a community of up to 200 household consumers in the UK show that the newly proposed method can achieve very close redistribution to the exact Shapley values but at a much lower (and practically feasible) computation cost. Furthermore, it performed similarly to the probabilistic, state-of-the-art approximation method while having smaller time complexity as well as other desirable characteristics for cost redistribution in energy communities.

The goal of seismic imaging is to create a model of the subsurface from samples of a transmitted wavefield that is reflected in soil layers. The created model can be used to locate storage possibilities for CO2 or H2 or to find oil and gas reservoirs or other natural resources. Seismic imaging relies on the propagation of wavefields, which can be computed by evaluating the Rayleigh integral, a process that often requires a lot of time and resources. In this thesis we develop methods to reduce error in the computation of the Rayleigh integral whilst remaining time-efficient. To achieve this we first give the derivation of the Rayleigh integral and provide a few methods to evaluate integrals numerically using interpolating polynomials. Afterwards, we adapt the integration methods to the Rayleigh integral and arrive at the main algorithms for its evaluation, at the end we compare these algorithms. We present the method that is currently used for the computation of the Rayleigh integral and a modification that extends the method to samples on a rectilinear grid. The adjusted version of this method did not perform consistently in our results, although it achieved better results than the original method on average. Secondly we present a combined interpolation method (that is, it interpolates the full integrand without taking advantage that one of the two functions in the integrand is known) named Simpson's rule, which only performed better in the high sample points per wavelength range with minimal noise. An alteration to the method for semi-equidistant grids also did not perform consistently and is not worth the extra operations. Next was the separate interpolation algorithm (this time taking advantage of the known part of the integrand), this method is difficult to implement and had only slightly better performance than the combined method. The final method was an extension of the separate interpolation algorithm to non-e, Applied Mathematics | Applied Physics

Multi-Level variants of classic optimisation problems are becoming more noteworthy as the complexity of real life applications increases. In this research we investigate the Multi-Level Bin Packing optimisation problem, which models, for example, global logistics and part manufacturing. We will look at the performance of solving Integer Linear Programming formulations of the Multi-Level Bin Packing problem using IBM ILOG CPLEX Optimization Studio, and compare these results to the performance of simple heuristic-based algorithms to reach conclusions about the usefulness of optimal-solution algorithms for NP-Hard problems. We ultimately find that the simple heuristics leave a large gap in optimality, while the solving time for finding optimal solutions is still too large for practical instances. As such, we conclude that more specialised algorithms are needed that can balance the time cost and optimality, depending on the application., CSE3000 Research Project, Computer Science and Engineering

Submodular functions characterize mathematically the ubiquitous ``diminishing-returns'’ property. They are widely used to describe core subjects in numerous applications, including economic utility, redundancy in information, spread of influence in social networks, and more. Optimization of submodular functions thus plays a central role in a broad range of applications in data science. However, existing works concentrate largely on optimizing a single submodular function, with a sole focus on succinct subset selection among massive data. Other circumstances have not been fully explored, for example, when there exists interplay between a submodular function and other components. In this thesis, we study optimization beyond a single (non-decreasing) submodular function in the following three areas. Ranking: Ranking arises naturally in the presence of multiple submodular functions, for instance, when a list of shared resources is sequentially served to satisfy multiple submodular demands with individual budgets. One concrete example is ranking web pages to satisfy multiple user intents with different ``patience.'' We first study this ranking problem under cardinality constraints, and then we consider extensions of the basic setting, including knapsack constraints, streaming settings, and robustness requirements. Decision trees: A tree (or a policy) can be seen as an adaptive generalization of ranking. Popular decision trees for classification, including CART and C4.5, are constructed by recursive greedy splits, guided by some impurity function. These trees are accurate, but may not be easy to understand due to a potentially large tree size. A novel characterization of a decision tree is via adaptive intersection among multiple submodular functions, one for each object to be classified. We discover that this characterization enables one to analyze and control the tree complexity for a large family of impurity functions. As a consequence, we are able to produce accurate, Submodulära funktioner karakteriserar matematiskt den allestädes närvarande egenskapen ``minskande avkastning''. De används ofta för att beskriva kärnämnen i många tillämpningar, inklusive ekonomisk nytta, redundans i information, spridning av inflytande i sociala nätverk och mer. Optimering av submodulära funktioner spelar således en central roll i ett brett spektrum av tillämpningar inom datavetenskap. Befintliga arbeten koncentrerar sig dock till stor del på att optimera en enda submodulär funktion, med enbart fokus på kortfattat urval av delmängder bland massiva data. Andra omständigheter har inte undersökts fullt ut, till exempel när det finns ett samspel mellan en submodulär funktion och andra komponenter. I denna avhandling studerar vi optimering bortom en enda (icke-minskande) submodulär funktion inom följande tre områden. Ranking: Rangordning uppstår naturligt i närvaro av flera submodulära funktioner, till exempel när en lista med delade resurser serveras sekventiellt för att tillfredsställa flera submodulära krav med individuella budgetar. Ett konkret exempel är att rangordna webbsidor för att tillfredsställa flera användares avsikter med olika ``tålamod''. Vi studerar först detta rankningsproblem under kardinalitetsbegränsningar, och sedan överväger vi utökningar av den grundläggande inställningen, inklusive ryggsäcksbegränsningar, strömningsinställningar och robusthetskrav. Beslutsträd: Ett träd (eller en policy) kan ses som en adaptiv generalisering av rangordning. Populära beslutsträd för klassificering, inklusive CART och C4.5, är konstruerade av rekursiva giriga splittringar, styrda av någon orenhetsfunktion. Dessa träd är korrekta, men kanske inte är lätta att förstå på grund av en potentiellt stor trädstorlek. En ny karaktärisering av ett beslutsträd sker via adaptiv skärningspunkt mellan flera submodulära funktioner, en för varje objekt som ska klassificeras. Vi upptäcker att denna karakterisering gör det möjligt för en att analysera och kontroll, QC 20221220

The number of offspring and the population size greatly influence the performance of the Plant Propagation Algorithm, a crossover-less metaheuristic, when applied to the Euclidean traveling salesman problem. However, with large volumes of experimental data, a clearly characterizable relation emerges, facilitating both an exact parameterization as well as opening up perspectives on a precisely predictable outcome. These results directly question its position between exact, approximation, and PTAS algorithms. Although the metaheuristic is thereby officially parameter sensitive when deployed to the Euclidean traveling salesman problem, it does appear to be largely insensitive to different problem instances. This is very different from earlier results on continuous optimization, which were completely opposite. Why is that, and what does it mean for our practices in algorithmic benchmarking?

Recently, Udwani defined a new class of set functions under monotonicity and subadditivity, called submodular order functions, which is a subfamily of submodular functions. Informally, the submodular order function admits a very limited form of submodularity which is defined over a specific permutation of the ground set. His work pointed out the intriguing connection between streaming submodular maximization and submodular order maximization. Inspired by a 0.25-approximation streaming algorithm for maximizing a monotone submodular function subject to a matroid constraint, Udwani gave a 0.25-approximation algorithm for submodular order functions maximization subject to a matroid constraint. Based on the above results, we would like to explore further in which cases it is feasible to generalize from streaming submodular maximization algorithms to submodular order maximization algorithms. As a more general constraint than matroid, p-matchoid is a collection of p matroids with each matroid defined on some subsets of the ground set. Related work gave a 1/4p-approximation streaming algorithm for monotone submodular functions maximization under a p-matchoid constraint. Inspired by the above algorithms and the intriguing connection, we used some techniques to try to generalize several streaming algorithms for submodular functions to the offline algorithms for submodular order functions, including interleaved partitions and incremental values. Assuming that the objective function f is subadditive and non-negative, we gave a 1/4p-approximation algorithm for monotone submodular order maximization to a p-matchoid constraint. In addition, we summarize the failures of other cases., Nyligen definierade Udwani en ny klass av mängdfunktioner under monotonicitet och subadditivitet, som kallas submodulära ordningsfunktioner och som är en underfamilj av submodulära funktioner. Informellt sett medger den submodulära ordningsfunktionen en mycket begränsad form av submodularitet som är definierad över en specifik permutation av grundmängden. Hans arbete pekade på det spännande sambandet mellan strömmande submodulär maximering och submodulär ordermaximering. Inspirerad av en strömningsalgoritm med 0.25-approximation för maximering av en monoton submodulär funktion som är föremål för en matroidbegränsning, gav Udwani en algoritm med 0.25-approximation för maximering av submodulära ordningsfunktioner som är föremål för en matroidbegränsning. Baserat på ovanstående resultat skulle vi vilja utforska ytterligare i vilka fall det är möjligt att generalisera från algoritmer för strömning av submodulära maximeringsfunktioner till algoritmer för maximering av submodulära orderfunktioner. Som en mer allmän begränsning än matroid är p-matchoid en samling av p matroider där varje matroid definieras på vissa delmängder av grundmängden. Relaterade arbeten gav en strömmingsalgoritm med 1/4p-tillnärmning för monoton submodulär funktionsmaximering under en p-matchoid-begränsning. Inspirerade av ovanstående algoritmer och det spännande sambandet använde vi vissa tekniker för att försöka generalisera flera strömningsalgoritmer för submodulära funktioner till offline-algoritmer för submodulära ordningsfunktioner, inklusive interleaved partitions och inkrementella värden. Under förutsättning att målfunktionen f är subadditiv och icke-negativ gav vi en algoritm för 1/4p-tillnärmning för monoton submodulär ordermaximering till ett p-matchoid-begränsningsvillkor. Dessutom sammanfattar vi misslyckanden i andra fall.

Decision trees are popular classification models, providing high accuracy and intuitive explanations. However, as the tree size grows the model interpretability deteriorates. Traditional tree-induction algorithms, such as C4.5 and CART, rely on impurity-reduction functions that promote the discriminative power of each split. Thus, although these traditional methods are accurate in practice, there has been no theoretical guarantee that they will produce small trees. In this paper, we justify the use of a general family of impurity functions, including the popular functions of entropy and Gini-index, in scenarios where small trees are desirable, by showing that a simple enhancement can equip them with complexity guarantees. We consider a general setting, where objects to be classified are drawn from an arbitrary probability distribution, classification can be binary or multi-class, and splitting tests are associated with non-uniform costs. As a measure of tree complexity, we adopt the expected cost to classify an object drawn from the input distribution, which, in the uniform-cost case, is the expected number of tests. We propose a tree-induction algorithm that gives a logarithmic approximation guarantee on the tree complexity. This approximation factor is tight up to a constant factor under mild assumptions. The algorithm recursively selects a test that maximizes a greedy criterion defined as a weighted sum of three components. The first two components encourage the selection of tests that improve the balance and the cost-efficiency of the tree, respectively, while the third impurity-reduction component encourages the selection of more discriminative tests. As shown in our empirical evaluation, compared to the original heuristics, the enhanced algorithms strike an excellent balance between predictive accuracy and tree complexity., QC 20221214

Submodular maximization has been the backbone of many important machine-learning problems, and has applications to viral marketing, diversification, sensor placement, and more. However, the study of maximizing submodular functions has mainly been restricted in the context of selecting a set of items. On the other hand, many real-world applications require a solution that is a ranking over a set of items. The problem of ranking in the context of submodular function maximization has been considered before, but to a much lesser extent than item-selection formulations. In this paper, we explore a novel formulation for ranking items with submodular valuations and budget constraints. We refer to this problem as max-submodular ranking (MSR). In more detail, given a set of items and a set of non-decreasing submodular functions, where each function is associated with a budget, we aim to find a ranking of the set of items that maximizes the sum of values achieved by all functions under the budget constraints. For the MSR problem with cardinality- and knapsack-type budget constraints we propose practical algorithms with approximation guarantees. In addition, we perform an empirical evaluation, which demonstrates the superior performance of the proposed algorithms against strong baselines., QC 20221214

Bayesian networks are popular probabilistic models that capture the conditional dependencies among a set of variables. Inference in Bayesian networks is a fundamental task for answering probabilistic queries over a subset of variables in the data. However, exact inference in Bayesian networks is NP-hard, which has prompted the development of many practical inference methods. In this paper, we focus on improving the performance of the junction-tree algorithm, a well-known method for exact inference in Bayesian networks. In particular, we seek to leverage information in the workload of probabilistic queries to obtain an optimal workload-aware materialization of junction trees, with the aim to accelerate the processing of inference queries. We devise an optimal pseudo-polynomial algorithm to tackle this problem and discuss approximation schemes. Compared to state-of-the-art approaches for efficient processing of inference queries via junction trees, our methods are the first to exploit the information provided in query workloads. Our experimentation on several real-world Bayesian networks confirms the effectiveness of our techniques in speeding-up query processing., QC 20221214

Submodular functions characterize mathematically the ubiquitous ``diminishing-returns'’ property. They are widely used to describe core subjects in numerous applications, including economic utility, redundancy in information, spread of influence in social networks, and more. Optimization of submodular functions thus plays a central role in a broad range of applications in data science. However, existing works concentrate largely on optimizing a single submodular function, with a sole focus on succinct subset selection among massive data. Other circumstances have not been fully explored, for example, when there exists interplay between a submodular function and other components. In this thesis, we study optimization beyond a single (non-decreasing) submodular function in the following three areas. Ranking: Ranking arises naturally in the presence of multiple submodular functions, for instance, when a list of shared resources is sequentially served to satisfy multiple submodular demands with individual budgets. One concrete example is ranking web pages to satisfy multiple user intents with different ``patience.'' We first study this ranking problem under cardinality constraints, and then we consider extensions of the basic setting, including knapsack constraints, streaming settings, and robustness requirements. Decision trees: A tree (or a policy) can be seen as an adaptive generalization of ranking. Popular decision trees for classification, including CART and C4.5, are constructed by recursive greedy splits, guided by some impurity function. These trees are accurate, but may not be easy to understand due to a potentially large tree size. A novel characterization of a decision tree is via adaptive intersection among multiple submodular functions, one for each object to be classified. We discover that this characterization enables one to analyze and control the tree complexity for a large family of impurity functions. As a consequence, we are able to produce accurate, Submodulära funktioner karakteriserar matematiskt den allestädes närvarande egenskapen ``minskande avkastning''. De används ofta för att beskriva kärnämnen i många tillämpningar, inklusive ekonomisk nytta, redundans i information, spridning av inflytande i sociala nätverk och mer. Optimering av submodulära funktioner spelar således en central roll i ett brett spektrum av tillämpningar inom datavetenskap. Befintliga arbeten koncentrerar sig dock till stor del på att optimera en enda submodulär funktion, med enbart fokus på kortfattat urval av delmängder bland massiva data. Andra omständigheter har inte undersökts fullt ut, till exempel när det finns ett samspel mellan en submodulär funktion och andra komponenter. I denna avhandling studerar vi optimering bortom en enda (icke-minskande) submodulär funktion inom följande tre områden. Ranking: Rangordning uppstår naturligt i närvaro av flera submodulära funktioner, till exempel när en lista med delade resurser serveras sekventiellt för att tillfredsställa flera submodulära krav med individuella budgetar. Ett konkret exempel är att rangordna webbsidor för att tillfredsställa flera användares avsikter med olika ``tålamod''. Vi studerar först detta rankningsproblem under kardinalitetsbegränsningar, och sedan överväger vi utökningar av den grundläggande inställningen, inklusive ryggsäcksbegränsningar, strömningsinställningar och robusthetskrav. Beslutsträd: Ett träd (eller en policy) kan ses som en adaptiv generalisering av rangordning. Populära beslutsträd för klassificering, inklusive CART och C4.5, är konstruerade av rekursiva giriga splittringar, styrda av någon orenhetsfunktion. Dessa träd är korrekta, men kanske inte är lätta att förstå på grund av en potentiellt stor trädstorlek. En ny karaktärisering av ett beslutsträd sker via adaptiv skärningspunkt mellan flera submodulära funktioner, en för varje objekt som ska klassificeras. Vi upptäcker att denna karakterisering gör det möjligt för en att analysera och kontroll, QC 20221220

Network slicing is a promising approach for enabling low latency computation offloading in edge computing systems. In this paper, we consider an edge computing system under network slicing in which the wireless devices generate latency sensitive computational tasks. We address the problem of joint dynamic assignment of computational tasks to slices, management of radio resources across slices and management of radio and computing resources within slices. We formulate the Joint Slice Selection and Edge Resource Management (JSS-ERM) problem as a mixed-integer problem with the objective to minimize the completion time of computational tasks. We show that the JSS-ERM problem is NP-hard and develop an approximation algorithm with bounded approximation ratio based on a game theoretic treatment of the problem. We use extensive simulations to provide insight into the performance of the proposed solution from the perspective of the whole system and from the perspective of individual slices. Our results show that the proposed slicing policy can achieve significant gains compared to the equal slicing policy, and that the computational complexity of the proposed task placement algorithm is approximately linear in the number of devices., Not duplicate with DiVA 1426002QC 20221129

Emerging advanced System-on-Chip (SoC) designs contain more and more complicated functions to be accelerated. This presents a challenge to conventional design approaches which use different hardware architectures or separate hardware accelerators to implement the various functions. To tackle this challenge, for the first time, we propose a generalized hardware accelerator called 'Huicore' to speed up diverse functions on the same substrate. Through the analysis and transformation of mathematical characteristics, we reveal the commonality of many complicated functions using the CORDIC algorithm. Then we explore a reconfigurable architecture to implement them. The proposed reconfigurable accelerator can not only accelerate the implementation of many complicated functions, but also has small area, low power consumption and high precision. It is very suitable for integration in a SoC system to accelerate the implementation of various applications., QC 20221121

In this paper, an open-source solver for mixed-integer nonlinear programming (MINLP) problems is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) combines a dual strategy based on polyhedral outer approximations (POA) with primal heuristics. The POA is achieved by expressing the nonlinear feasible set of the MINLP problem with linearizations obtained with the extended supporting hyperplane (ESH) and extended cutting plane (ECP) algorithms. The dual strategy can be tightly integrated with the mixed-integer programming (MIP) subsolver in a so-called single-tree manner, i.e., only a single MIP optimization problem is solved, where the polyhedral linearizations are added as lazy constraints through callbacks in the MIP solver. This enables the MIP solver to reuse the branching tree in each iteration, in contrast to most other POA-based methods. SHOT is available as a COIN-OR open-source project, and it utilizes a flexible task-based structure making it easy to extend and modify. It is currently available in GAMS, and can be utilized in AMPL, Pyomo and JuMP as well through its ASL interface. The main functionality and solution strategies implemented in SHOT are described in this paper, and their impact on the performance are illustrated through numerical benchmarks on 406 convex MINLP problems from the MINLPLib problem library. Many of the features introduced in SHOT can be utilized in other POA-based solvers as well. To show the overall effectiveness of SHOT, it is also compared to other state-of-the-art solvers on the same benchmark set., QC 20221031

When searching for information in a data collection, we are often interested not only in finding relevant items, but also in assembling a diverse set, so as to explore different concepts that are present in the data. This problem has been researched extensively. However, finding a set of items with minimal pairwise similarities can be computationally challenging, and most existing works striving for quality guarantees assume that item relatedness is measured by a distance function. Given the widespread use of similarity functions in many domains, we believe this to be an important gap in the literature. In this paper we study the problem of finding a diverse set of items, when item relatedness is measured by a similarity function. We formulate the diversification task using a flexible, broadly applicable minimization objective, consisting of the sum of pairwise similarities of the selected items and a relevance penalty term. To find good solutions we adopt a randomized rounding strategy, which is challenging to analyze because of the cardinality constraint present in our formulation. Even though this obstacle can be overcome using dependent rounding, we show that it is possible to obtain provably good solutions using an independent approach, which is faster, simpler to implement and completely parallelizable. Our analysis relies on a novel bound for the ratio of Poisson-Binomial densities, which is of independent interest and has potential implications for other combinatorial-optimization problems. We leverage this result to design an efficient randomized algorithm that provides a lower-order additive approximation guarantee. We validate our method using several benchmark datasets, and show that it consistently outperforms the greedy approaches that are commonly used in the literature., QC 20220930

Online social networks provide a forum where people make new connections, learn more about the world, get exposed to different points of view, and access information that were previously inaccessible. It is natural to assume that content-delivery algorithms in social networks should not only aim to maximize user engagement but also to offer opportunities for increasing connectivity and enabling social networks to achieve their full potential. Our motivation and aim is to develop methods that foster the creation of new connections, and subsequently, improve the flow of information in the network. To achieve our goal, we propose to leverage the strong triadic closure principle, and consider violations to this principle as opportunities for creating more social links. We formalize this idea as an algorithmic problem related to the densest k-subgraph problem. For this new problem, we establish hardness results and propose approximation algorithms. We identify two special cases of the problem that admit a constant-factor approximation. Finally, we experimentally evaluate our proposed algorithm on real-world social networks, and we additionally evaluate some simpler but more scalable algorithms., QC 20220921