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This study describes two types of algorithms for skid-to-turn unmanned aerial vehicles to plan paths between two waypoints under constant wind conditions. The first type of algorithm is a rigorous optimization algorithm based on the Euler-Lagrange formulation with analytical integration of the path. The second type of algorithm is a fast algorithm describing the path by two circular arcs connected by a line segment or another circular arc in the air mass frame, which is similar to the Dubins path. The latter algorithm is developed for actual airborne application, whereas the former algorithm is developed to check the quasi-optimality of the path calculated by the latter algorithm. We present a convergence proof of the latter algorithm under certain assumptions and its quasi-optimality in comparison with the former algorithm. Furthermore, the computational efficiency and the convergence reliability of the latter algorithm are demonstrated through numerical examples.

The Frank-Wolfe algorithm has been extensively adopted in recent decades to solve the user-equilibrium problem because of its simple structure and low memory requirements. However, Dial observed that the results obtained by the Frank-Wolfe algorithm differed markedly from the B algorithm of Dial in terms of link flows, and the results obtained via Frank-Wolfe algorithm could be incorrect. This study attempts to provide a clear example showing that the Frank-Wolfe algorithm has difficulty in achieving an ϵ-user equilibrium state when ϵ is sufficiently small. An Augmented Frank-Wolfe algorithm is presented that overcomes the weaknesses of the conventional arc-based Frank-Wolfe algorithm.

In this paper, an algorithm for sensitivity analysis for equilibrium traffic network flows with link interferences is proposed. Based on this sensitivity analysis algorithm, a general algorithm is provided for solving the optimal design and management problems for traffic networks. In particular, this algorithm is applied to the optimal traffic signal setting problem. A numerical example is given to demonstrate the effectiveness of our algorithm.

The maximum flow problem is one of the classic combinatorial optimization problems with many applications, such as electrical powers, traffics, communications, computer networks and logistics. The problem is to find a flow of maximum value on a network from a source to a sink. Ordered binary decision diagram (OBDD) is a canonical form to represent and manipulate the Boolean functions efficiently. OBDD-based symbolic algorithms appear to give improved results for large-scale combinatorial optimization problems by searching the nodes and edges implicitly. For the maximum flow problem in networks, we present the symbolic algebraic decision diagram (ADD) formulation and symbolic algorithms. The augmenting-path-based symbolic algorithm is the combination of the Gabow's scaling algorithm with the binary decision diagram (BDD)-based symbolic algorithm for the maximum flow in 0–1 networks. The Karzanov's algorithm is implemented implicitly, resulting in the preflow-based symbolic algorithm (PSA), in which the vertices on each layer of the layered networks are partitioned by the vertex's input preflow and the total capacity of its outgoing edges, and the edges to push or pull the preflow are selected in terms of the priority function. The improved PSA is developed by integrating the heuristic of Traff's algorithm and the assistant layered networks into the PSA. The symbolic algorithms do not require explicit enumeration of the nodes and edges, and therefore can handle large-scale networks.

A new hybrid genetic algorithm was developed which combines a stochastic evolutionary algorithm with a deterministic adaptive step steepest descent hill climbing algorithm in order to optimize complex multivariate problems. By combining both algorithms computational resources are conserved and the solution converges rapidly as compared to either algorithm alone. In genetic algorithms natural selection is mimicked by random events such as breeding and mutation. In the adaptive step steepest descent algorithm the solution moves toward the lowest surrounding point. Step sizes start big and get progressively smaller, increasing computational efficiency. The genetic algorithm ensures the solution samples the entire global search space, thus a global minimum is found. The steepest descent method fine tunes the solution by moving it to the nearest local minimum. The code was developed, including a graphical user interface, in MATLAB. Additional features such as bounding the input, weighting the objective functions individually, and constraining the output are also built into the interface. The algorithm developed was used to optimize the response surface models which use process variables (feedstock moisture content, die speed, and preheating temperature) to predict pellet properties (pellet moisture content, unit, bulk and tapped density, durability, and specific energy consumption). The solution found by the hybrid algorithm was validated experimentally. Execution times were decreased by approximately 40%, based on 1,0000 trials with each method, using the new hybrid algorithm as compared to using a genetic algorithm alone with the same parameters, both developed at INL. Performance of the hybrid algorithm versus the commercial Matlab genetic algorithm is investigated. Results show that the hybrid genetic algorithm converged to the global maximum for bulk density in one iteration, whereas the commercial genetic algorithm took twenty nine iterations to converge.

In this paper, the algorithm of network maximum flow based on network flow matrix is introduced first, then some new properties of network flow matrix are studied according to max-flow min-cut theorem, and on this basis the improved algorithm of network maximum flow based on network flow matrix is given. In this way, the matrix can be reduced order directly when it satisfies certain particular conditions and be translated into several matrices when its order is large, thus simplifying the original algorithm.

This paper presents an algorithm for finding a global minimum of a multimodal, multivariate and nondifferentiable function. The algorithm is a modification to the new version of the Price's algorithm given in Brachetti et al. [J. Global Optim. 10, 165---184 (1997)]. Its distinguishing features include: (1) The number-theoretic method is applied to generate the initial population so that the points in the initial population are uniformly scattered, and therefore the algorithm could explore uniformly the region of interest at the initial iteration; (2) The simplified quadratic approximation with the three best points is employed to improve the local search ability and the accuracy of the minimum function value, and to reduce greatly the computational overhead of the algorithm. Two sets of experiments are carried out to illustrate the efficiency of the number-theoretic method and the simplified quadratic model separately. The proposed algorithm has also been compared with the original one by solving a wide set of benchmark problems. Numerical results show that the proposed algorithm requires a smaller number of function evaluations and, in many cases, yields a smaller or more accurate minimum function value. The algorithm can also be used to deal with the medium size optimization problems.

This paper presents a continuation and optimization based algorithm to detect power flow unsolvability. In addition, the algorithm obtains the power flow solution, if it exists, no matter how ill-conditioned the power system is. The proposed algorithm is based on the parameterization of the distance from the starting point to the real power flow to be solved, using a convergence margin. The performance of the algorithm is illustrated considering an highly loaded scenario of the operation of the Spanish power system.

The author introduces a minimum cost maximum flows (MCMF) routing algorithm that allows the construction of a multicast tree that incorporates both static and dynamic nodes. The key idea of the algorithm is, first, finding the least delay path of the partial static tree (PST) from a source node to a set of static receivers, by using the ratio of "delay/number of flows" as cost function; and second, adding the dynamic nodes to the constructed PST, one by one, according to their arrival order, by minimizing the ratio "delay/number of flows." According to the presented simulation, this algorithm is superior to shortest path tree (SPT) technique and minimum delay maximum degree algorithm (MDMDA). This result is obtained according to certain simulation parameters and to the tool used to construct the graphs, regarding the total tree cost and the total tree flows criteria, when there is no delay constraint.

An algorithm for the longest-path subproblem in the network algorithm of Mehta and Patel for Fisher’s exact test in two-way contingency tables is proposed. Use of the primaldual technique for convex-cost flows and the maximum likelihood estimate makes the algorithm more efficient in time and space than existing algorithms.

Fujishige proposed a polynomial-time maximum flow algorithm using maximum adjacency (MA) orderings. Computational results by Fujishige and Isotani showed that the algorithm was slower in practice than Goldberg and Tarjan's algorithm. In this paper we propose an improved version of Fujishige's algorithm using preflows. Our computational results show that the improved version is much faster than the original one in practice.

This paper presents a new strongly polynomial cut canceling algorithm for minimum cost submodular flow. The algorithm is a generalization of our similar cut canceling algorithm for ordinary min-cost flow. The algorithm scales a relaxed optimality parameter and creates a second, inner relaxation that is a kind of submodular max flow problem. The outer relaxation uses a novel technique for relaxing the submodular constraints that allows our previous proof techniques to work. The algorithm uses the min cuts from the max flow subproblem as the relaxed most positive cuts it chooses to cancel. We show that this algorithm needs to cancel only ${\mathrm O}(n^3)$ cuts per scaling phase, where $n$ is the number of nodes. Furthermore, we show how to slightly modify this algorithm to get a strongly polynomial running time. Finally, we briefly show how to extend this algorithm to the separable convex cost case and that the same technique can be used to construct a polynomial time maximum mean cut canceling algorithm for submodular flow.

The scheduling problems studied in this paper concern the two-stage no-wait flowshops with parallel machines under the objective function of the minimization of the maximum completion time. A new heuristic algorithm, i.e., the minimum deviation algorithm, is developed to solve the problems. In order to evaluate the average case performance of the algorithm, we design numerical experiments to compare the effectiveness of the algorithm with that of the other approximation algorithms. Extensive simulations are conducted under different shop conditions, and the results statistically show that the minimum deviation algorithm performs well under most of the situations.

First, we present two classes of sequential algorithms for minimum flow problem: decreasing path algorithms and preflow algorithms. Then we describe another approach of the minimum flow problem, that consists of applying any maximum flow algorithm in a modified network. In section 5 we present several parallel preflow algorithms that solve the minimum flow problem. Finally, we present an application of the minimum flow problem.

Quite recently, Fujishige (Oper. Res. Lett. 31 (2003) 176-178) developed a weakly polynomial-time algorithm for the maximum flow problem by applying the maximum adjacency (MA) ordering technique to directed networks. In this note, we show that the algorithm is not strongly polynomial by giving a real-valued instance for which the algorithm does not terminate.

An algorithm called genetic shortest-path algorithm is presented to solve capacitated minimal Steiner tree problems in graphs with complex flows and arbitrary arc cost functions, but without negative cycles. Voltage constraint can also been taken into consideration by the algorithm. Hence, it can solve various power distribution system optimization problems with detailed mathematical models. In the proposed algorithm, a local optimization method based on shortest-path algorithm and heuristics is used to find the local optimums, in which the minimum cost objective and all constraints are considered and the specialties of the problems are made good use of. Genetic operations are only used to search the global optimum from the local optimums. Therefore, this algorithm overcomes the disadvantage of general genetic algorithm in local searching. An example for distribution system planning problem with large scale is given to demonstrate the power of the algorithm.

An independent set is a useful structure because, in some situations, it defines a set of mutually compatible operations, i.e., operations that can be executed simultaneously. We design a fault-containing self-stabilizing algorithm that finds a maximal independent set for an asynchronous distributed system. Our algorithm is an improvement on the self-stabilizing algorithm in Shukla et al. [1995]. In the single-fault situation, the worst-case stabilization time of Shukla's algorithm is /spl Omega/(n), where n is the number of nodes in the system, whereas the worst-case stabilization time of our algorithm is O(/spl Delta/), where /spl Delta/ is the maximum node degree in the system. Compared also with the fault-containing algorithm that is induced from applying the general transformer in Ghosh et al. [1996] to Shukla's algorithm, our algorithm is also seen to be faster in stabilization time, in the single-fault situation. Therefore, our algorithm can be considered to be the most efficient fault-containing self-stabilizing algorithm for the maximal independent set finding up to this point.

We propose two flow control algorithms for networks with multiple paths between each source-destination pair. Both are distributed algorithms over the network to maximize aggregate source utility. Algorithm 1 is a first order Lagrangian method applied to a modified objective function that has the same optimal solution as the original objective function but has a better convergence property. Algorithm 2 is based on the idea that, at optimality, only paths with the minimum price carry positive flows, and naturally decomposes the overall decision into flow control (determines total transmission rate based on minimum path price) and routing (determines how to split the flow among available paths). Both algorithms can be implemented as simply a source-based mechanism in which no link algorithm nor feedback is needed. We present numerical examples to illustrate their behavior.

An incremental algorithm may yield an enormous computational time saving to solve a network flow problem. It updates the solution to an instance of a problem for a unit change in the input. In this paper we have proposed an efficient incremental implementation of maximum flow problem after inserting an edge in the network G. The algorithm has the time complexity of O((Δn)2m), where Δn is the number of affected vertices and m is the number of edges in the network. We have also discussed the incremental algorithm for deletion of an edge in the network G.

We study computing maximum flows for real-worldnetworks. In contrast to prior studies, our implementation is bulksynchronous. Our algorithm applies push and relabel operationson all active vertices in parallel, and maintains a preflow througha delayed flow update approach with handshakes between flowpushing and flow receiving.In our implementation the heuristics are no longer entangledwith the push and relabel operations as in prior implementations.We apply two heuristics well known for the sequential algorithm,that is, global relabel and gap relabel, to our parallel implementation.Experiments on networks constructed for computer visionimages show that our parallel implementation on the target 8-core machine is up to 8.6 times faster than the best sequentialimplementation.We aslo propose a new augmenting path based heuristic forsmall-world graphs. On large social networks with up to billionsof edges our implementation achieves close to 40 times parallelspeedup.

In order to raise solving speed of the two-dimensional open dimension optimization algorithm, an improved parallel algorithm based on BSBIS algorithm is proposed, namely p-BSBIS. To overcome the defect of BSBIS algorithm which spends long time for complexity of the algorithm, p-BSBIS can shorten the packing time to a certain extent by using multiple nodes for parallel computing. Furthermore, the improved algorithm not only increases the operation speed but also retains accurate optimization of the original BSBIS. Simulated in the platform, the results demonstrated that p-BSBIS is better than the original algorithm for solving speed.

The network problems multi-terminal flow, minimum cost flow, and multicommodity flow are fundamental to network design and performance evaluation. The first two can be solved exactly by the Gomory-Hu and the out-of-kilter algorithms, respectively. The former is a combinatorial algorithm on graph cuts, and the latter a primal-dual method. Multi-commodity flow is NP-complete for integer flows, and even for real-valued flows it is rather complex. Even if it in principle can be solved by linear programming, the number of constraints grow very fast with the problem size. An approximate method is therefore presented, which is suitable also for large problem instances.

This paper is concerned with an efficient global optimization algorithm for solving a kind of fractional program problem(P), whose objective and constraints functions are all defined as the sum of ratios generalized polynomial functions. The proposed algorithm is a combination of the branch-and-bound search and two reduction operations, based on an equivalent monotonic optimization problem of(P). The proposed reduction operations specially offer a possibility to cut away a large part of the currently investigated region in which the global optimal solution of(P)does not exist, which can be seen as an accelerating device for the solution algorithm of(P). Furthermore, numerical results show that the computational efficiency is improved by using these operations in the number of iterations and the overall execution time of the algorithm, compared with other methods. Additionally, the convergence of the algorithm is presented, and the computational issues that arise in implementing the algorithm are discussed. Preliminary indications are that the algorithm can be expected to provide a practical approach for solving problem(P)provided that the number of variables is not too large.

Abstract Some special cases of the Maximum Flow Problem under nonnegative lower bounds on arc flows are investigated. Assuming that at least one of these bounds is strictly positive, a class of problems has been identified for which a single phase algorithm suffices to prove optimality. This situation contrasts with the two phases algorithm which is commonly used in the literature to solve these problems. In spite of having the same overall complexity of the two phases algorithm, the single phase one appears to be, computationally speaking, more attractive.

We present an algorithm for solving the minimum-cut problem on closure graphs without maintaining flow values. The algorithm is based on an optimization algorithm for the open-pit mining problem that was presented in 1964 (and published in 1965) by Lerchs and Grossmann. The Lerchs—Grossmann algorithm (LG algorithm) solves the maximum closure which is equivalent to the minimum-cut problem. Yet, it appears substantially different from other algorithms known for solving the minimum-cut problem and does not employ any concept of flow. Instead, it works with sets of nodes that have a natural interpretation in the context of maximum closure in that they have positive total weight and are closed with respect to some subgraph. We describe the LG algorithm and study its features and the new insights it reveals for the maximum-closure problem and the maximum- flow problem. Specifically, we devise a linear time procedure that evaluates a feasible flow corresponding to any iteration of the algorithm. We show that while the LG algorithm is pseudopolynomial, our variant algorithms have complexity of O(mn log n), where n is the number of nodes and m is the number of arcs in the graph. Modifications of the algorithm allow for efficient sensitivity and parametric analysis also running in time O(mn log n). © 2001 John Wiley & Sons, Inc.

Goldberg and Rao recently proposed the blocking flow method based on a binary length function to obtain a better algorithm for the maximum flow problem. The previous algorithms based on the blocking flow method proposed by Dinic use the unit length function: every residual edge is of length 1. In this paper, we survey properties of the distance function defined by a length function and give an overview on the representative maximum flow algorithms proposed so far in a systematic way by utilizing these properties. Among them are included two new algorithms: the Goldberg-Rao algorithm which finds a maximum flow on an integral capacity network N of n vertices and m edges in ~(min{ml/~, n2/3}7n log(n2/m) log U) time, where U is the maximum edge capacity of N, and the Karger-Levine algorithm which finds a maximum flow on an undirected network N with unit capacity and no parallel edges in 0(m + nv3/2) time, where v is the value of a maximum flow of N.

In this paper, we present a new polynomial time algorithm for solving the minimum cost network flow problem. This algorithm is based on Edmonds-Karp's capacity scaling and Orlin's excess scaling algorithms. Unlike these algorithms, our algorithm works directly with the given data and original network, and dynamically adjusts the scaling factor between scaling phases, so that it performs at least one flow augmentation in each phase. Our algorithm has a complexity of O(m(m+nlogn)log(B/(m+n))), where n is the number of nodes, m is the number of arcs, and B is the sum of the finite arc capacities and supplies in the network.

The minimum cost flow problem is to determine a least cost shipment of a commodity through a network G = (N, A) in order to satisfy demands at certain nodes from available supplies at other nodes. In this paper, we study a variant of the minimum cost flow problem where we are given a set R ⊆ A of arcs and require that each arc in R must carry the same amount of flow. This problem, which we call the simple equal flow problem, arose while modeling a water resource system management in Sardinia, Italy. We consider the simple equal flow problem in a directed network with n nodes, m arcs, and where all arc capacities and node supplies are integer and bounded by U. We develop several algorithms for the simple equal flow problem—the network simplex algorithm, the parametric simplex algorithm, the combinatorial parametric algorithm, the binary search algorithm, and the capacity scaling algorithm. The binary search algorithm solves the simple equal flow problem in O(log(nU)) applications of any minimum cost flow algorithm. The capacity scaling algorithm solves it in O(m(m + n logn) log (nU)) time, which is almost the same time needed to solve the minimum cost flow problem by the capacity scaling algorithm. These algorithms can be easily modified to obtain an integer solution of the simple equal flow problem.

The Stoer‐Wagner algorithm computes a minimum cut in a weighted undirected graph. The algorithm works inn 1 phases, wheren is the number of nodes ofG. Each phase takes time O.mCn logn/ ,w herem is the number of edges ofG, and computes a pair of vertices s and t and a minimum cut separatings and t . We show how to extend the algorithm such that each phase also computes a maximum flow from s tot . The flow is computed in O.m/ additional time and certifies the cut computed in the phase. © 1999 Elsevier Science B.V. All rights reserved. We give a correctness certificate for the min-cut algorithm of Stoer and Wagner [6]. This algorithm refines the algorithm of Nagamochi and Ibaraki [5,4]; it has the same time complexity, but is simpler. The algorithm is deterministic. There are faster randomized algorithms [2,3]. No certificates are known for the randomized algorithms. Let G be an undirected graph with n vertices and m edges. The algorithm of Stoer and Wagner works inn 1 phases. In each phase it identifies two vertices and a minimum cut separating them and then collapses the two vertices into one. The global min-cut is the minimum cut found in any phase. Each phase runs in time O.mCn logn/. We extend the algorithm such that it also finds a flow equal to the min-cut in each phase. The additional time required to find the flow is O.m/ in each phase.

We present an alternate linear algorithm for finding the minimum flow in (s, t)-planar networks using a new concept of minimal removable sets developed here. The iterative nature of the algorithm facilitates the adjustment of solutions for systems in developmental stages. The minimum flow algorithm presented here requires O(|V|) time, where V denotes the set of vertices. The minimum flow problem arises in many transportation and communication systems.

An important advantage of the proposed algorithm compared with previous algorithms is that it easily finds the maximum flow between a given pair of network nodess, t. This requires onlym repetitions of the algorithm, wherem is the number of edges in the graphG defining the given network. The time complexity of finding the maximum flow by the proposed algorithm thus does not exceed O(mn). The procedure to find the maximum flow consists of two steps.

Query optimization of database management systems is aimed at finding an optimal access path for a query to minimize the evaluation cost. This research addresses the problem of query optimization for databases in which objects frequently change their values. A greedy, adaptive query optimization algorithm is proposed to evaluate relational queries and queries containing complex objects. Rather than constructing a full plan for an access path and executing it, the algorithm constructs a partial plan, executes it, updates the statistics, and constructs a new partial plan. Since a partial plan is constructed based on the latest statistics, the algorithm is adaptive to data modifications and errors from the statistics. It is proved that the algorithm can produce an optimal solution for a class of queries. Furthermore, experiments show that the overhead associated with the algorithm is negligible and the algorithm is efficient for other cases. An adaptive query optimization algorithm for distributed environments is also proposed. The algorithm extends the SDD-1 algorithm to local area networks by considering local processing cost as well as communication cost. Whereas the SDD-1 algorithm only uses semi-joins to reduce communication cost, the algorithm reduces it with joins as well. It is proved that the adaptive algorithm is more efficient than the SDD-1 algorithm.

The maximum flow algorithm is distinguished by the long line of successive contributions researchers have made in obtaining algorithms with incrementally better worst-case complexity. Some, but not all, of these theoretical improvements have produced improvements in practice. The purpose of this paper is to test some of the major algorithmic ideas developed in the recent years and to assess their utility on the empirical front. However, our study differs from previous studies in several ways. Whereas previous studies focus primarily on CPU time analysis, our analysis goes further and provides detailed insight into algorithmic behavior. It not only observes how algorithms behave but also tries to explain why algorithms behave that way. We have limited our study to the best previous maximum flow algorithms and some of the recent algorithms that are likely to be efficient in practice. Our study encompasses ten maximum flow algorithms and five classes of networks. The augmenting path algorithms tested by us include Dinic's algorithm, the shortest augmenting path algorithm, and the capacity-scaling algorithm. The preflow-push algorithms tested by us include Karzanov's algorithm, three implementations of Goldberg-Tarjan's algorithm, and three versions of Ahuja-Orlin-Tarjan's excess-scaling algorithms. Among many findings, our study concludes that the preflow-push algorithms are substantially faster than other classes of algorithms, and the highest-label preflow-push algorithm is the fastest maximum flow algorithm for which the growth rate in the computational time is O ( n 1.5 ) on four out of five of our problem classes. Further, in contrast to the results of the worst-case analysis of maximum flow algorithms, our study finds that the time to perform relabel operations (or constructing the layered networks) takes at least as much computation time as that taken by augmentations and/or pushes.

We propose a strongly polynomial algorithm for the minimum cost tension problem. Our algorithm is inspired by Goldberg and Tarjan's ideas which deal with the minimum cost circulation problem. It consists of repeatedly canceling minimum mean-cost residual cuts. Hence, we had to consider two other combinatorial optimization problems which possess interesting practical applications: the min-cost and min-mean-cost residual cut problems (Hadjiat and Maurras, 1995).

In this paper, we consider maximum integral flow problems with an additional reverse convex constraint involving one or two nonlinear variables. Based on a parametric approach, we propose a polynomial-time algorithm for computing an integral flow globally optimal to the problem with a single nonlinear variable. We extend this idea and solve the problem with two nonlinear variables. The algorithm solves a sequence of ordinary minimum cost flow problems by using a conventional method and yields a globally optimal solution in pseudo-polynomial time.

Data generated in sensor networks may have different importance and priority. Different types of data contribute differently for scientists to analyze the physical environment. In a challenging environment, wherein sensor nodes do not always have connected paths to the base station, and not all the data can be preserved inside the network due to severe energy constraints and storage constraints at sensor nodes, how to preserve data with maximum priority is a new and challenging problem. In this paper, we study how to preserve data that yield maximum total priorities, under the constraints that each sensor node has limited energy level and storage capacity. We design an efficient optimal algorithm and prove its optimality. The core of the problem is a maximum weighted flow problem, which is to maximize the total weight of flow in the network considering different flows have different weights. Maximum weighted flow is a generalization of the classic maximum flow problem, wherein each unit of flow has the same weight. To the best of our knowledge, our work is the first to study and solve the maximum weighted flow problem. We propose a more time efficient heuristic algorithm. Via simulation, we show that it performs comparably to the optimal algorithm and performs better than the classic maximum flow algorithm, which does not consider data priority. Finally we design a distributed data preservation algorithm based on push-relabel algorithm, analyze its time and message complexities, and empirically show that it outperforms the push-relabel distributed maximum flow algorithm in terms of the total preserved priorities.

We present the first combinatorial polynomial time algorithm for computing the equilibrium of the Arrow-Debreu market model with linear utilities. Our algorithm views the allocation of money as flows and iteratively improves the balanced flow as in [Devanur et al. 2008] for Fisher's model. We develop new methods to carefully deal with the flows and surpluses during price adjustments. In our algorithm, we need O(n6log(nU)) maximum flow computations, where n is the number of persons and U is the maximum integer utility, and the length of the numbers is at most O(nlog(nU)) to guarantee an exact solution. The previous polynomial time algorithms [Nenakov and Primak 1983, Jain 2007, Ye 2007] for this problem are based on solving convex programs using the ellipsoid algorithm or interior-point method.

A general optimal control algorithm, which is approximately second-order, is presented. It is essentially an infinite-dimensional version of the Han-Powell algorithm. It is shown that this algorithm generates a descent direction of an exact penalty function. Finally, it is shown that the algorithm is globally convergent in the sense that every accumulation point of the sequence generated by the algorithm,satisfies a "weak version" of Pontryagin's Minimum Principle. A numerical example is given.

In this paper, modified versions of the classical deterministic maximum flow and minimum cost network flow problems are presented in a stochastic queueing environment. In the maximum flow network model, the throughput rate in the network is maximized such that for each arc of the network the resulting probability of finding congestion along that arc in excess of a desirable threshold does not exceed an acceptable value. In the minimum cost network flow model, the minimum cost routing of a flow of given magnitude is determined under the same type of constraints on the arcs. After proper transformations, these models are solved by Ford and Fulkerson's labeling algorithm and out-of-kilter algorithm, respectively.

Most existing algorithms for parallel or distributed reduction operations are not able to handle temporary or permanent link and node failures. Only recently, methods were proposed which are in principal capable of tolerating link and node failures as well as soft errors like bit flips or message loss. A particularly interesting example is the pushflow algorithm. However, on closer inspection, it turns out that in this method the failure recovery often implies severe performance drawbacks. Existing mechanisms for failure handling may basically lead to a fall-back to an early stage of the computation and consequently slow down convergence or even prevent convergence if failures occur too frequently. Moreover, state-of-the-art fault tolerant distributed reduction algorithms may experience accuracy problems even in failure free systems. We present the push-cancel-flow (PCF) algorithm, a novel algorithmic enhancement of the push-flow algorithm. We show that the new push-cancel-flow algorithm exhibits superior accuracy, performance and fault tolerance over all other existing distributed reduction methods. Moreover, we employ the novel PCF algorithm in the context of a fully distributed QR factorization process and illustrate that the improvements achieved at the reduction level directly translate to higher level matrix operations, such as the considered QR factorization.

It is shown that the problem of finding theK best solutions of a linear integer network flow problem can be solved by a polynomial time algorithm. This algorithm can be used in order to solve a multiple-criteria network flow problem which minimizes the maximum ofQ objectives.

In this paper an algorithm is given to obtain cuts from paths of a 2-state reliability system. The new algorithm is based on set theoretic considerations. It improves the algorithm of Elias, Mokhles and Ibrahim. An example is given to demonstrate the algorithm.

Maximum adjacency (MA) ordering has effectively been applied to graph connectivity problems by Nagamochi and Ibaraki. In this note we show an application of MA ordering to the maximum flow problem with integral capacities to get a new polynomial-time algorithm. A scaling version of our algorithm runs in O(mnlogU) time, where m is the number of arcs, n the number of vertices, and U the maximum capacity.

The paper points out the relationship between the bottleneck and the minimum cutset of the network, and presents a capacity expansion algorithm of network optimization to solve the network bottleneck problem. The complexity of the algorithm is also analyzed. As required by the algorithm, some virtual sources are imported through the whole positive direction subsection in the network, in which a certain capacity value is given. Simultaneously, a corresponding capacity-expanded network is constructed to search all minimum cutsets. For a given maximum flow value of the network, the authors found an adjustment value of each minimum cutset arc’s group with gradually reverse calculation and marked out the feasible flow on the capacity-extended networks again with the adjustment value increasing. All this has been done repeatedly until the original topology structure is resumed. So the algorithm can increase the capacity of networks effectively and solve the bottleneck problem of networks.

Efficient retrieval of replicated data from multiple disks is a challenging problem. Traditional retrieval techniques assume that replication is done at a single site using homogeneous disk arrays having no initial load or network delay. Recently, generalized retrieval algorithms are proposed to cover heterogeneous disk arrays, initial loads, and network delays. Generalized retrieval algorithms achieve the optimal response time retrieval schedule by performing multiple runs of a maximum flow algorithm. Since the maximum flow algorithm is used as a black box technique, flow values of the previous runs cannot be conserved to speed up the process. In this paper, we propose integrated maximum flow algorithms for the generalized optimal response time retrieval problem. Our first algorithm uses Ford-Fulkerson method and the second algorithm uses Push-relabel algorithm. Besides the sequential implementations, a multi-threaded version of the push-relabel algorithm is also implemented. Proposed algorithms are investigated using various replication schemes, query types, query loads, disk specifications, and system delays. Experimental results show that the sequential integrated push-relabel algorithm runs up to 2.5X faster than the black box version. Furthermore, parallel integrated push-relabel implementation achieves up to 1.7X speed up (~1.2X on average) over the sequential algorithm using two threads, which makes the integrated algorithm up to 4.25X (~3X on average) faster than its black box counterpart.

International audience; A minimum cost maximum flow algorithm is proposed for resources (e.g. virtual machines) placement in clouds confronted to dynamic workloads and flows variations. The algorithm is compared to an exact method generalizing the classical Bin-Packing formulation using a linear integer program. A directed graph is used to model the allocation problem for cloud resources organized in a finite number of resource types; a common practice in cloud services. Providers can use the minimum cost maximum flow algorithm to opportunistically select the most appropriate physical resources to serve applications or to ensure elastic platform provisioning. The modified Bin-Packing algorithm is used to benchmark the minimum cost maximum flow solution. The latter combined with a prediction mechanism to handle dynamic variations achieves near optimal performance.

There are lots of steps and complicated calculation in the existing algorithm for solving the maximum flow,and because of improper selection order of augmented path, we cannot obtain the ideal maximum flow. In order to solve these problems in existing algorithm, this paper make some improvement of the existing algorithms, then puts forward a new improved algorithm for solving the maximum flow problem which make use of divide area and the degree of vertex. And it is verified that the improved algorithm is effective and intuitive through the concrete example, and avoid the labeling process, the entire operation process only needs drawing a diagram to be completed.