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The data surveying this study mines methods for extracting informative and interesting knowledge from learning student datasets. The amount of data stored in education big databases is growing at an alarming rate. As such, data processing and knowledge discovery techniques can be used to discover interesting relationships between different characteristics and assessments of students. Initially to propose a novel self-analysis model which performs analysis about the different big data learning services. From the result provided by the user, the service will be ranked and analyze about the knowledge from daily activity gathered by the learner. The proposed model performs analysis to provide efficient Educational Data Mining (EDM) E-Learning system based on machine learning to ranking the users and performance evaluation in their activities. The existing method does not consider the learner activities, ranking and it focus on single feature based classification so the system doesn’t provide a better classification result. These issues to overcome introduce an Extended Multi-Labeled Gradient Boosting (XMGB) improve the classification performance both of imbalanced dataset. The method initial stage apply the Adaptive Expectation-Maximization Mixture (AEMM) method cluster the data various group and extract the E-learning multiple feature set. In this method to compute the classification time and memory provide an efficient result. Then introduce an academic activity based weight score analysis model to evaluate the learner daily activates and exam score its help to the ranking and cluster the data groups. In this proposed method analysis result to evaluate the following performance matrix: Recall, precision, F measure, classification accuracy. In this simulation analysis of the proposed method XMGB are provide an efficient classification with less time complexity compared to other existing methods.

Density-Based clustering are the main clustering algorithms because they can cluster data with different shapes and densities, but some of these algorithms have high time complexity like OPTICS (Ordering Points to Identify Clustering Structure) and DBSCAN (Density-based spatial clustering of applications with noise) where the time complexity up to O( n 2 ). In this paper, we use an approach to reduce this complexity by providing fuzzy clusters to OPTICS, which make the process of finding neighbours within an only narrow region (fuzzy group) instead of searching all the state space making the algorithm faster than the original one with keeping almost the same accuracy of the innovative algorithm. The results show that there is an improvement in execution time using some synthetic and real datasets with high dimensions.

Interval and proper interval graphs are very well-known graph classes, for which there is a wide literature. As a consequence, some generalizations of interval graphs have been proposed, in which graphs in general are expressed in terms of $k$ interval graphs, by splitting the graph in some special way. As a recent example of such an approach, the classes of $k$-thin and proper $k$-thin graphs have been introduced generalizing interval and proper interval graphs, respectively. The complexity of the recognition of each of these classes is still open, even for fixed $k \geq 2$. In this work, we introduce a subclass of $k$-thin graphs (resp. proper $k$-thin graphs), called precedence $k$-thin graphs (resp. precedence proper $k$-thin graphs). Concerning partitioned precedence $k$-thin graphs, we present a polynomial time recognition algorithm based on $PQ$-trees. With respect to partitioned precedence proper $k$-thin graphs, we prove that the related recognition problem is \NP-complete for an arbitrary $k$ and polynomial-time solvable when $k$ is fixed. Moreover, we present a characterization for these classes based on threshold graphs., 33 pages

Hole-twins – graphs that arise when a vertex is added to a hole in such a way to form a twin with some vertex of the hole – were discussed in a recent paper by Dai, Foley, and Hoang where it was shown that there is a polynomial time algorithm to color ( c l a w , 4 K 1 , hole-twin)-free graphs. We continue our investigation of hole-twin-free graphs and show the coloring problem for ( c l a w , P 7 , hole-twin)-free graphs is also polynomial-time solvable.

The present study focuses on designing the memory-based sampled data control approach to achieve the desired performance from switched-type of neural networks. The overall contribution of the study can be viewed from two directions. The first part is to derive the theoretical-based sufficient stability conditions that ensure the synchronization of uncontrolled and controlled systems. The idea behind the synchronization analysis is because of time complexity and computational cost. Once, we derive the closed-loop system then user can employ them in any practical application without interruptions. The existence of time-delays during the information transmission is inevitable, and in a practical sense, the delays, which are a function of time are well-effective. Besides, the sufficient conditions are derived in terms of solvable linear matrix inequalities (LMIs), which can be solved to ensure the global asymptotical stability of the error system, derived from uncontrolled–controlled systems. Technically, the work integrates with the new type of discontinuous Lyapunov–Krasovskii functional candidate with integral terms, several delay-dependent stability conditions, and Wirtinger-based integral inequality. The second part works on utilizing the controlled system into a real-life application, say, encryption/decryption process. To an evident, the proposed controlled system is considered as crypto-system in the encryption/decryption process.

Graph planning gives rise to fundamental algorithmic questions such as shortest path, traveling salesman problem, etc. A classical problem in discrete planning is to consider a weighted graph and construct a path that maximizes the sum of weights for a given time horizon $T$. However, in many scenarios, the time horizon is not fixed, but the stopping time is chosen according to some distribution such that the expected stopping time is $T$. If the stopping time distribution is not known, then to ensure robustness, the distribution is chosen by an adversary, to represent the worst-case scenario. A stationary plan for every vertex always chooses the same outgoing edge. For fixed horizon or fixed stopping-time distribution, stationary plans are not sufficient for optimality. Quite surprisingly we show that when an adversary chooses the stopping-time distribution with expected stopping time $T$, then stationary plans are sufficient. While computing optimal stationary plans for fixed horizon is NP-complete, we show that computing optimal stationary plans under adversarial stopping-time distribution can be achieved in polynomial time. Consequently, our polynomial-time algorithm for adversarial stopping time also computes an optimal plan among all possible plans.

We present a generalization of a combinatorial result by Aggarwal et al. (1989) on a linear-time algorithm that selects a constant fraction of leaves, with pairwise disjoint neighborhoods, from a binary tree embedded in the plane. This result of Aggarwal et al. (1989) is essential to the linear-time framework, which they also introduced, that computes certain Voronoi diagrams of points with a tree structure in linear time. An example is the diagram computed while updating the Voronoi diagram of points after deletion of one site. Our generalization allows that only a fraction of the tree leaves is considered, and it is motivated by research on linear time construction algorithms for Voronoi diagrams of non-point sites. We are given a plane tree T of n leaves, m of which have been marked, and each marked leaf is associated with a neighborhood (a subtree of T ) such that any two topologically consecutive marked leaves have disjoint neighborhoods. We show how to select in linear time a constant fraction of the marked leaves having pairwise disjoint neighborhoods.

The eternal vertex cover problem is a variant of the classical vertex cover problem defined in terms of an infinite attacker–defender game played on a graph. In each round of the game, the defender reconfigures guards from one vertex cover to another in response to a move by the attacker. The minimum number of guards required in any winning strategy of the defender when this game is played on a graph G is the eternal vertex cover number of G , denoted by evc ( G ) . It is known that given a graph G and an integer k , checking whether evc ( G ) ≤ k is NP-hard. Further, it is known that for any graph G , mvc ( G ) ≤ evc ( G ) ≤ 2 mvc ( G ) , where mvc ( G ) is the vertex cover number of G . Though a characterization is known for graphs for which evc ( G ) = 2 mvc ( G ) , a characterization of graphs for which evc ( G ) = mvc ( G ) remained as an open problem, since 2009. We achieve such a characterization for a class of graphs that includes chordal graphs and internally triangulated planar graphs. For biconnected chordal graphs, our characterization leads to a polynomial time algorithm for precisely determining evc ( G ) and an algorithm for determining a safe strategy for guard movement in each round of the game using only evc ( G ) guards. Though the eternal vertex cover problem is only known to be in PSPACE in general, it follows from our new characterization that the problem is in NP for locally connected graphs, a graph class which includes all biconnected internally triangulated planar graphs. We also provide reductions establishing NP-completeness of the problem for biconnected internally triangulated planar graphs. As far as we know, this is the first NP-completeness result known for the problem for any graph class.

In this paper, we study the Cartesian product of signed graphs as defined by Germina, Hameed and Zaslavsky (2011). Here we focus on its algebraic properties and look at the chromatic number of some Cartesian products. One of our main results is the unicity of the prime factor decomposition of signed graphs. This leads us to present an algorithm to compute this decomposition in linear time based on a decomposition algorithm for oriented graphs by Imrich and Peterin (2018). We also study the chromatic number of a signed graph, that is the minimum order of a signed graph to which the input signed graph admits a homomorphism, of graphs with underlying graph of the form P n □ P m , of Cartesian products of signed paths, of Cartesian products of signed complete graphs and of Cartesian products of signed cycles.

An Italian dominating function on a simple undirected graph G is a function f : V ( G ) ⟶ { 0 , 1 , 2 } satisfying the condition that for each vertex v with f ( v ) = 0 , ∑ u ∈ N G ( v ) f ( u ) ≥ 2 . An Italian dominating function f on G is called a perfect Italian dominating function on G if for each vertex v with f ( v ) = 0 , ∑ u ∈ N G ( v ) f ( u ) = 2 . The weight of a function f on a graph G , denoted by w ( f ) , is the sum ∑ v ∈ V ( G ) f ( v ) . For a simple undirected graph G , Min-PIDF is the problem of finding the minimum weight of a perfect Italian dominating function on G . First, we discuss the complexity difference between Min-PIDF and the problem of finding the minimum weight of an Italian dominating function. We then establish the NP -completeness of the decision version of Min-PIDF in chordal graphs and investigate the hardness of approximation of Min-PIDF in general graphs. Finally, we present linear time algorithms for computing the minimum weight of a perfect Italian dominating function in block graphs and series-parallel graphs.

In an undirected graph, a matching cut is a partition of vertices into two sets such that the edges across the sets induce a matching. The Matching Cut problem is the problem of deciding whether a given graph has a matching cut. Let H be a fixed undirected graph. A vertex coloring of an undirected input graph G is said to be an H - Free Coloring if none of the color classes contain H as an induced subgraph. The H - Free Chromatic Number of G is the minimum number of colors required for an H - Free Coloring of G . Both The Matching Cut problem and the H - Free Coloring problem can be expressed using a monadic second-order logic (MSOL) formula and hence is solvable in linear time for graphs with bounded tree-width. However, this approach leads to a running time of f ( | | φ | | , t ) n O ( 1 ) , where | | φ | | is the length of the MSOL formula, t is the tree-width of the graph and n is the number of vertices of the graph. The dependency of f ( | | φ | | , t ) on | | φ | | can be as bad as a tower of exponentials. In this paper, we provide explicit combinatorial FPT algorithms for Matching Cut problem and H - Free Coloring problem, parameterized by the tree-width of G . The single exponential FPT algorithm for the Matching Cut problem answers an open question posed by Kratsch and Le (2016). The techniques used in the paper are also used to provide an FPT algorithm for a variant of H -free coloring, where H is forbidden as a subgraph (not necessarily induced) in the color classes of G .

The nullity of a vertex-weighted graph is equal to the number of zero eigenvalues of its adjacency matrix. In this article, we give a linear time algorithm to calculate the nullity of vertex-weighted block graphs, i.e., graphs in which every block is a clique, with weights assigned to the vertices.

The problem of computing induced subgraphs that satisfy some specified restrictions arises in various applications of graph algorithms and has been well studied. In this paper, we consider the following Balanced Connected Subgraph (shortly, BCS) problem. The input is a graph $G=(V,E)$, with each vertex in the set $V$ having an assigned color, "red" or "blue". We seek a maximum-cardinality subset $V'\subseteq V$ of vertices that is color-balanced (having exactly $|V'|/2$ red nodes and $|V'|/2$ blue nodes), such that the subgraph induced by the vertex set $V'$ in $G$ is connected. We show that the BCS problem is NP-hard, even for bipartite graphs $G$ (with red/blue color assignment not necessarily being a proper 2-coloring). Further, we consider this problem for various classes of the input graph $G$, including, e.g., planar graphs, chordal graphs, trees, split graphs, bipartite graphs with a proper red/blue $2$-coloring, and graphs with diameter $2$. For each of these classes either we prove NP-hardness or design a polynomial time algorithm., 15 pages, 3 figures

In an observational study, one is given disjoint samples of treatment units and control (untreated) units, and the goal is to compare outcomes between the two samples in order to estimate a treatment effect. A complication is that the treatment and control units often differ on important pre-treatment attributes, and these differences, referred to as covariate imbalance, can bias the estimate. One method to correct for covariate imbalance is to select a subset of the control sample that has minimum imbalance with respect to the treatment sample, and then use this control subset for estimating the treatment effect. While this optimization problem is NP-hard in general, certain special cases can be solved efficiently. Specifically, the variant of this optimization problem with one covariate is easy to solve, the variant with three or more covariates is NP-hard, and the variant with two covariates is solvable in polynomial time. We present several network flow formulations for the problem of minimizing imbalance on two nominal covariates. First, we present a minimum cost network flow formulation for solving the problem with the constraint that the control subset must have the same size as the treatment sample. We then derive an improved maximum flow formulation. For alternate size restrictions on the control subset, we use a proportional imbalance objective which leads to non-integral supplies and demands in the preceding network flow formulations. We then derive an alternate minimum cost network flow formulation that ensures integrality and solves the proportional imbalance problem in polynomial time.

This work proposes an exact solution approach for the two-machine robust flow shop problem, where operation processing times are uncertain and vary in a given interval. Based on the concept of budgeted uncertainty, the objective is to obtain a robust scheduling that minimizes the makespan of the restricted worst-case scenario, where only a subset of job processing times will oscillate to their worst-case values. To our knowledge, this is the first work to obtain optimal solutions to this problem, by extending two classical MILP formulations for the deterministic case and combining them with a Column-and-Constraint Generation framework. For this purpose, a dynamic programming algorithm was also developed, allowing the identification of worst-case scenarios in polynomial time. Experiments on a set of literature instances confirm the efficacy of our approach, including a case study that shows little overhead in the expected solution value of obtained robust solutions.

In this paper, we consider a probability maximizing shortest path problem. For a given directed graph with the length of each arc being an independent normal random variable with rational mean and standard deviation, the problem is to find a simple s − t path that maximizes the probability of arriving at the destination within a given limit. We first prove that the problem is NP -hard even on directed acyclic graphs with the mean of the length of each arc being restricted to an integer. Then, we present pseudo-polynomial time exact algorithms for the problem along with nontrivial special cases that can be solved in polynomial time. Finally, we present a fully polynomial approximation scheme (FPTAS) that iteratively solves deterministic shortest path problems. The structure of the proposed approximation scheme can be applied to devise FPTAS for other probability maximizing combinatorial optimization problems once the corresponding deterministic problems are polynomially solvable.

It is well known that the treewidth of a graph G corresponds to the node search number where a team of searchers is pursuing a fugitive that is lazy and invisible (or alternatively is agile and visible) and has the ability to move with infinite speed via unguarded paths. Recently, monotone and connected node search strategies have been considered. A search strategy is monotone if it prevents the fugitive from pervading again areas from where he had been expelled and is connected if, at each step, the set of vertices that is or has been occupied by the searchers induces a connected subgraph of G . It has been shown that the corresponding connected and monotone search number of a graph G can be expressed as the connected treewidth, denoted by ctw ( G ) , that is defined as the minimum width of a rooted tree-decomposition ( X , T , r ) , where the union of the bags corresponding to the nodes of a path of T containing the root r is connected in G . In this paper, we initiate the algorithmic study of connected treewidth. We design a O ( n 2 ⋅ log n ) -time dynamic programming algorithm to compute the connected treewidth of biconnected series–parallel graphs. At the price of an extra n factor in the running time, our algorithm generalizes to graphs of treewidth at most two.

The diffusion method is one of the main methods of community detection in complex networks. In this method, the use of the concept that diffusion within the nodes that are members of a community is faster than the diffusion of nodes that are not in the same community. In this way, the dense subgraph will detect the graph in the middle layer. The LPA algorithm, which mimics epidemic contagion by spreading labels, has attracted much attention in recent years as one of the most efficient algorithms in the subcategory of diffusion methods. This algorithm is one of the detection algorithms of most popular communities in recent years because of possessing some advantages including linear time order, the use of local information, and non-dependence on any parameter; however, due to the random behavior in LPA, there are some problems such as unstable and low quality resulting from larger monster communities. This algorithm is easily adaptable to attributed network. In this paper, it is supposed to propose a new version of the LPA algorithm for attributed graphs so that the detected communities solve the problems related to unstable and low quality in addition to possessing structural cohesiveness and attribute homogeneity. For this purpose, a weighted graph of the combination of node ​​attributes and topological structure is produced from an attributed graph for nodes which have edges with each other. Also, the centrality of each node will be calculated equal to the influence of each node using Laplacian centrality, and the steps of selecting the node are being enhanced for updating as well as the mechanism of updating based on the influence of nodes. The proposed method has been compared to other primary and new attributed graph clustering algorithms for real and artificial datasets. In accordance with the results of the experiments on the proposed algorithm without parameter adjusting for different networks of density and entropy criteria, the normalized mutual information indicates that the proposed method is more efficient and precise than other state-of-the-art attributed graph clustering methods.

Consider a region that requires to be protected from unauthorized penetrations. The border of the region, modeled as a unit line segment, consists of high priority segments that require the highest level of protection separated by low priority segments that require to be visited infinitely often. We study the problem of patrolling the border with a set of k robots. The goal is to obtain a strategy that minimizes the maximum idle time (the time that a point is left unattended) of the high priority points while visiting the low priority points infinitely often. We use the concept of single lid cover (segments of fixed length) where each high priority point is covered with at least one lid, and then we extend it to strong double-lid cover where each high priority point is covered with at least two lids, and the unit line segment is fully covered. Let λk-1 be the minimum lid length that accepts a single λk-1-lid cover with k - 1 lids and Λ2k be the minimum lid length that accepts a strong double Λ2k-lid cover with 2k lids. We show that 2min(Λ2k, λk-1) is the lower bound of the idle time when the max speed of the robots is one. To compute Λ2k and λk-1, we present an algorithm with time complexity O(max(k, n) logn) where n is the number of high priority sections. Our algorithm improves by a factor of min(n, k) the previous O(knlogn) running time algorithm. For the upper bound, first we present a strategy with idle time λk-1 where one robot covers the unit line, and the remaining robots cover the lids of a single λk-1-lid cover with k - 1 lids. Then, we present a simple strategy with idle time 3Λ2k that splits the unit line into not-disjoint k segments of equal length that robots synchronously cover, i.e., reaching the leftmost and rightmost point simultaneously. Then, we present a complex strategy that split the unit line into k non-disjoint segments that robots asynchronously cover. We show that combining strategies one and two attain an approximation of 1.5 the optimal idle time and combining strategy one and third attain optimal idle time.

Classifier ensembles are characterized by the high quality of classification, thanks to their generalizing ability. Most existing ensemble algorithms use all learning samples to learn the base classifiers that may negatively impact the ensemble’s diversity. Also, the existing ensemble pruning algorithms often return suboptimal solutions that are biased by the selection criteria. In this work, we present a proposal to alleviate these drawbacks. We employ an instance selection method to query a reduced training set that reduces both the space complexity of the formed ensemble members and the time complexity to classify an instance. Additionally, we propose a guided search-based pruning schema that perfectly explores large-size ensembles and brings on a near-optimal subensemble with less computational requirements in reduced memory space and improved prediction time. We show experimentally how the proposed method could be an alternative to large-size ensembles. We demonstrate how to form less-complex, small-size, and high-accurate ensembles through our proposal. Experiments on 25 datasets show that the proposed method can produce effective ensembles better than Random Forest and baseline classifier pruning methods. Moreover, our proposition is comparable with the Extreme Gradient Boosting Algorithm in terms of accuracy.

In this paper, we address the challenges of frequent backup and recovery operations associated with an unstable energy supply in energy-harvesting nonvolatile processors (NVPs). To address this problem, this paper adopts a retention state, which can allow the system to retain data in a volatile cache to wait for power recovery instead of immediately backing up the data. In addition, in an energy-harvesting NVP, important issues include how to back up and recover data, how to perform cache replacement, and how to transmit data to different parts of the cache in such a way that the performance and energy consumption can be improved and a successful backup can be guaranteed. Therefore, we propose a performance-oriented cache management scheme based on a retention state to generate near-optimal data migration, replacement and backup solutions for applications in polynomial time. This scheme uses two energy thresholds to pre-back up and back up data to reduce the backup and recovery operations according to the retention state. We evaluate the performance and energy consumption of our proposed algorithms in comparison with those of the dual-threshold SLC STT-RAM scheme and morphable cache scheme. The evaluation shows that the proposed scheme can achieve 18.58% and 4.54% lower average energy consumption than the SLC STT-RAM and morphable cache schemes, respectively, with comparable performance. The experimental results also show that compared with the SLC STT-RAM and morphable cache schemes, the proposed algorithm can achieve 17.90% and 8.85% performance improvement, respectively, on average.

It is proposed to tackle the problem of password leakage of popular websites like Linked-In, Adobe, Gmail, Yahoo, eHarmony, etc. by using dynamic password policy and enhanced hash algorithm. Here, an algorithm is developed that will generate password policies dynamically depending on the frequency of characters. Time complexity is computed, and it is found that the algorithm works fast. Since the algorithm creates password policies dynamically, it will be tough for the attacker to guess the characteristics of the password database.

The serving capabilities of networks are reduced by low-rate denial of service (LDoS) attacks that periodically send high-intensity pulse data flows. This type of attack shows a harmful effect similar to that of traditional DoS attacks, but their attack modes differ greatly. The high concealment of LDoS attacks makes it extremely difficult for traditional DoS detection methods to detect LDoS attacks. Meanwhile, the state-of-art detection methods for LDoS attacks have low-efficiency and resource-intensive and time complexity issues. We propose a novel detection method with analysis of abnormal network traffic under LDoS attacks that combines data mining technology. The judgement benchmarks were also established. The results from the experimental simulation on the simulated environment, physical environment and public datasets prove that the developed method can effectively detect LDoS attacks with optimal detection cost and low complexity, and has a high accuracy, a low false-negative rate, and a low false-positive rate.

Fault diagnosis plays an important role in maintaining the reliability of interconnection networks. Let v be a given node in an interconnection network G . v is conditionally locally t -diagnosable in G if the fault or fault-free status of node v can be identified correctly when the number of faults presented does not exceed t and every node has at least one healthy neighboring node. The conditional local diagnosis can be regarded as a local strategy toward the conditional diagnosis of networks, which puts more emphasis on identifying the status of a particular processor. In this paper, we first show a sufficient condition for a regular network to be conditionally locally t -diagnosable at a given node under the MM* model. As its applications, we derive the conditional diagnosability of hierarchical star network H S n etc. We also design an algorithm under the MM* model to identify the fault or fault-free status of a given processor in a regular network. According to our result, an α -regular network with a balanced three-tiered tree T ( v ; α , α − 1 , β ) rooted at v is conditionally locally ( 2 α + β − 3 ) -diagnosable at node v and the time complexity of our algorithm to diagnose v is o ( α 2 β 2 ) . As an application, we show our algorithm can identify the status of each node of star graph S n if the fault node number does not exceed 3 n − 9 . Compared with existing algorithms, our algorithm allows more faults to arise in a network.

Image denoising is a vital pre-processing phase, used to refine the image quality and make it more informative. Many image-denoising algorithms have been proposed with their own pros and cons. This paper presents a comprehensive study of the median filter and its different variants to reduce or remove the impulse noise from gray scale images. These filters are compared with respect to their functionality, time complexity and relative performance. For performance evaluation of the existing algorithms, extensive MATLAB based simulations have been carried out on a set of images. For benchmarking the relative performance, we have used Peak Signal to Noise Ratio (PSNR), Root Mean Square Error (RMSE), Universal Image Quality Index (UQI), Structural Similarity Index (SSIM) and Edge-strength Similarity (ESSIM) as quality assessment metrics. The Extended median filter (EMF) and Modified BDND are best in terms of relative statistical ratios and pleasant visual results where IAMF is having the best time complexity among existing algorithms.

The objective of cloud task scheduling is to partition tasks on shared resources to minimize energy consumption and makespan. Recently, several meta-heuristics for task scheduling were proposed and achieved encouraging results. However, their performance is far from the ideal state and needs more improvement. This paper introduces an enhanced sunflower optimization (ESFO) algorithm for improving the performance of existing task scheduling. It finds optimal scheduling in a polynomial time. The experiments show that ESFO outperformed its counterparts. The amount of improvement in comparison with the best counterpart is 0.73% and 2.24% respectively in terms of makespan and energy consumption.

Encryption schemes like AES require finite field modular multiplication. The encryption speed is highly dependent on the performance of the finite field multiplier. Several high-speed systolic bit parallel multipliers with low area complexity have been proposed in the literature. In this paper, a modular multiplication algorithm is used to propose a bit parallel polynomial basis systolic multiplier which has achieved 89% less and 17% less area-delay product than the best existing multipliers. It has been observed that the area complexity of the proposed systolic multiplier for irreducible polynomials matches with the best-reported multiplier with 17% less time complexity. The results are further verified with the help of the FPGA implementation of the proposed multiplier for m = 8,163. Being generic, the proposed multiplier can be optimized further for trinomials and pentanomials.

The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems. For instance, when enumerating minimal dominating sets of a graph $G=(V,E)$, one usually arrives at the problem to decide for a vertex set $U \subseteq V$, if there exists a \textit{minimal} dominating set $S$ with $U\subseteq S$. We propose a general, partial-order based formulation of such extension problems and study a number of specific problems which can be expressed in this framework. Possibly contradicting intuition, these problems tend to be NP-hard, even for problems where the underlying optimisation problem can be solved in polynomial time. This raises the question of how fixing a partial solution causes this increase in difficulty. In this regard, we study the parameterised complexity of extension problems with respect to parameters related to the partial solution, as well as the optimality of simple exact algorithms under the Exponential-Time Hypothesis. All complexity considerations are also carried out in very restricted scenarios, be it degree restrictions or topological restrictions (planarity) for graph problems or the size of the given partition for the considered extension variant of Bin Packing.

Weighted finite automata over the field of rational numbers and unary alphabets are considered. The notion of a characteristic polynomial is introduced for such automata as a means to provide a decidable necessary and sufficient condition, under which a unary weighted automaton admits a deterministic, i.e., sequential equivalent. The sequentiality problem for univariate rational series is thus proved to be decidable both over the rational numbers and over the integers, confirming a conjecture of S. Lombardy and J. Sakarovitch; its decidability over the nonnegative integers is observed as well. The decision algorithm proposed for these tasks is shown to run in polynomial time. A determinisation algorithm for determinisable unary weighted automata over the rational numbers is also described.

We give a linear-time algorithm to decide 3-colorability of a triangle-free graph embedded in a fixed surface, and a quadratic-time algorithm to output a 3-coloring in the affirmative case. The algorithms also allow to prescribe the coloring of a bounded number of vertices.

Dehazing is still a challenging problem for the outdoor images. The occurrence of haze, fog, mist etc., reduce the visibility of captured images in the outdoor environment. There are several dehazing techniques proposed to resolve the haze in the outdoor images but the existing techniques suffers from the computational time complexity. For a real-time application time complexity plays a major role. As a part of real-time application haze removal is done using the raspberry pi b+v1.2. The hazy image is restored by taking dark channel with patch size of 11 × 11 to avoid the oversaturation of recovered scene radiance and halo effect. Getting the image size and channels, the image is flattened to get the top bright points. Then the image is padded at the ends with a square of side of the window to get the minimum comparision at the ends. Because the atmospheric light to be taken from the foreground as the background has almost same pixel values distributed. The intensity is found, from that maximum among these pixels are found and considered for atmospheric light. The transmission map is found, hazy image is restored. And the performance of modified approach is compared with paper perception oriented haze image restoration based on physical optics model. Hence, to give a better dehazing images with reduced computational time using raspberry pi b+v1.2.

An edge clique partition of G is a set of edge-disjoint cliques of G which together contain every edge of G . In this work we investigate the computational complexity of determining the minimum size of an edge clique partition of G , denoted by c p ( G ) . This problem is NP-hard for split graphs and K 4 -free graphs. We establish a complete complexity classification of this problem on the hierarchy of ( k , l ) -graphs, graphs that can be partitioned into k independent sets and l complete sets. In addition, we determine in polynomial time the value of c p ( G ) for interesting subclasses of ( k , l ) -graphs: split-indifference graphs, partial 2-trees, and triangular grids.

The problem of finding anomalies and outliers in datasets is one of the most important challenges of modern data analysis. Among the commonly dedicated tools to solve this task one can find Isolation Forest (IF) that is an efficient, conceptually simple, and fast method. In this study, we propose the Probabilistic Generalization of Isolation Forest (PGIF) that is an intuitively appealing and efficient enhancement of the original approach. The proposed generalization is based on nonlinear dependence of segment-cumulated probability from the length of segment. Introduction of the generalization allows to achieve more effective splits that are rather performed between the clusters, i.e. regions where datapoints constitute dense formations and not through them. In a comprehensive series of experiments, we show that the proposed method allows us to detect anomalies hidden between clusters more effectively. Moreover, it is demonstrated that our approach favorably affects the quality of anomaly detection in both artificial and real datasets. In terms of time complexity our method is close to the original one since the generalization is related only to the building of the trees while the scoring procedure (which takes the main time) is kept unchanged.

In this note, we will devote to investigate the stability of discrete-time switched positive linear time-varying systems (PLTVSs). Firstly, a new asymptotic stability criterion of discrete-time PLTVSs is obtained by using time-varying copositive Lyapunov functions (TVCLFs) and this criterion is then extended to the switched case based on the multiple TVCLFs. Furthermore, the sufficient conditions are derived for stability of discrete-time switched PLTVSs with stable subsystems by means of function-dependent average dwell time and function-dependent minimum dwell time. In addition, the stability sufficient conditions are drawn for the switched PLTVSs which contain unstable subsystems. It is worth noting that the difference of TVCLFs and multiple TVCLFs are both relaxed to indefinite in our work. The theoretical results obtained are verified by two numerical examples.

Funding: The first author is supported by an Engineering and Physical Sciences Research Council grant (EP/P015638/1). The second author is supported by a Royal Society University Research Fellowship (URF\R\180015). Let H ≤ Sn be an intransitive group with orbits Ω1, Ω2, ... , Ωk. Then certainly H is a subdirect product of the direct product of its projections on each orbit, H|Ω1 x H|Ω2 x ... x H|Ωk. Here we provide a polynomial time algorithm for computing the finest partition P of the H-orbits such that H = Πc∈P H|c and we demonstrate its usefulness in some applications. Postprint

We consider facility location problems where n facilities are present in a convex polygon in the rectilinear plane, over which continuous and uniform demand is distributed and within which a convex polygonal barrier is located (removing all demand and preventing all travel within the barrier), and the optimal location for an additional facility is sought. We start with an in-depth analysis of the representation of the bisectors of two facilities affected by the barrier and how it is affected by the position of the additional facility. Following this, a detailed investigation into the changes in the structure of the Voronoi diagram caused by the movement of this additional facility, which governs the form of the objective function for numerous facility location problems, yields a set of linear constraints for a general convex barrier that partitions the market space into a finite number of regions within which the exact solution can be found in polynomial time. This allows us to formulate a polynomial exact algorithm that makes use of a triangular decomposition of the incremental Voronoi diagram and the first order optimality conditions.

The k -nearest-neighbor rule is a popular classification technique , and rough set theory is an effective mathematical tool to deal with the uncertainty of data. Rough set models based on k -nearest-neighbor relations have a strong ability to approximate decisions, but the calculation is very time-consuming. In this paper, we model the overlap degree of objects from different categories in advance to accelerate the attribute reduction and improve the classification performance of the selected attributes. Firstly, we define the coincidence degree ( CD ) and distance ( DIS ) of objects from different categories to measure the coverage and distance of between-class objects. Secondly, we combine CD and DIS to define the overlap degree ( OD ) to pre-sort attributes, then use k -nearest-neighbor rough sets to filter inconsistent and redundant attributes. The pre-sort operation based on OD can greatly reduce the number of searches for attributes and ensure that the attributes with high separability should be selected first. Furthermore, we design a fast reduction algorithm ( OD & KNN ) to obtain a reduct with the ability to approximate decisions as well as the original attributes but with lower OD . Comparing experimental results and time complexity of OD & KNN with state-of-the-art algorithms, OD & KNN is more efficient for high-dimensional data while ensuring classification accuracy .

Feature matching, which aims at seeking dependable correspondences between two sets of features, is of considerable significance to various vision-based tasks. This paper attempts to eliminate false correspondences from given tentative correspondences created on the basis of descriptor similarity. A simple yet efficient approach named neighborhood manifold representation consensus (NMRC) for robust feature matching is presented considering the stable neighborhood topologies of the potential true matches. The core principle of the proposed method is to preserve the local neighborhood structures between two feature points in a potential true match along a low-dimension manifold. Meanwhile, a neighborhood similarity-based iterative filtering strategy for neighborhood construction is designed to improve the matching performance under the circumstance of seriously deteriorated data. The matching problem is further formulated into a mathematical optimization model based on the neighborhood manifold representation and iterative filtering strategy, and a closed-form solution with linearithmic time complexity (i.e., O ( N log N ) ) is derived, which requires only tens of milliseconds to handle over 1000 putative correspondences. Extensive experiments on general feature matching (F-score > 94% for most cases), remote sensing image registration (RMSE

In this paper we present efficient algorithms to compute the radius, diameter, incenter, circumcenter, width and k dimensional enclosing cylinder for convex polyhedral and convex polyhedral offset distance functions in plane and in ℜ d for several types of inputs. We get optimal algorithms when the time complexities are linear. Let the size of input (convex polyhedron P /set S of points/convex polyhedra) be n / N , respectively, size of distance function convex polygon/polyhedron Q be m and size of constraint convex polyhedral region R be r in plane or ℜ d . The radius, incenter and circumcenter of the convex polygon P in ℜ 2 can be optimally computed in linear time, i.e. O ( n + m ) and in time O ( n + m + r ) , if the incenter or circumcenter is additionally constrained in a convex polygon/polyhedron R . In ℜ d , the radius, incenter and circumcenter of a convex polyhedron as well as of a set of convex polyhedra, unconstrained or constrained, can be computed in O ( N m ) and O ( N m + r ) time respectively, for convex constraint polyhedral region R . We also compute the minimum stabbing sphere for a set of convex polyhedra, unconstrained or constrained, for the above mentioned distance functions in O ( N m ) -time or O ( N m + r ) -time respectively for convex constraint polyhedral region R in ℜ d . The diameter of a convex polygon in plane can be computed in O ( n + m ) time and the diameter of a convex polyhedron in ℜ d can be computed in O ( n m ) time. The width of a convex polyhedron can be computed in O ( n + m ) time and O ( n 2 m ) time, for ℜ 2 and ℜ d , respectively. The diameter and width of a set of convex polyhedra can be computed in O ( N m ) -time and ( N 2 m ) , respectively, in any dimensions. We also show how the k dimensional minimum enclosing/stabbing cylinder for the convex polyhedron P can be computed in O ( n d − k + 2 m 2 ) in ℜ d and in O ( n d m ( n + m ) ) in ℜ d for k = 1 . The k dimensional minimum enclosing/stabbing cylinder for the set of convex polyhedra S in ℜ d can be computed in O ( N d − k + 2 m 2 ) -time. The diameter and width problems can also be solved for a set of points in ℜ d , either in time O ( n m ) or in time O ( m T ( n ) ) , where T ( n ) is the time complexity of the best convex hull computation algorithm for the given set of points.

Suppose an oracle knows a string $S$ that is unknown to us and that we want to determine. The oracle can answer queries of the form "Is $s$ a substring of $S$?". In 1995, Skiena and Sundaram showed that, in the worst case, any algorithm needs to ask the oracle $\sigma n/4 -O(n)$ queries in order to be able to reconstruct the hidden string, where $\sigma$ is the size of the alphabet of $S$ and $n$ its length, and gave an algorithm that spends $(\sigma-1)n+O(\sigma \sqrt{n})$ queries to reconstruct $S$. The main contribution of our paper is to improve the above upper-bound in the context where the string is compressible. We first present a universal algorithm that, given a (computable) compressor that compresses the string to $\tau$ bits, performs $q=O(\tau)$ substring queries; this algorithm, however, runs in exponential time. For this reason, the second part of the paper focuses on more time-efficient algorithms whose number of queries is bounded by specific compressibility measures. We first show that any string of length $n$ over an integer alphabet of size $\sigma$ with $rle$ runs can be reconstructed with $q=O(rle (\sigma + \log \frac{n}{rle}))$ substring queries in linear time and space. We then present an algorithm that spends $q \in O(\sigma g\log n)$ substring queries and runs in $O(n(\log n + \log \sigma)+ q)$ time using linear space, where $g$ is the size of a smallest straight-line program generating the string., Comment: Accepted for publication in Theoretical Computer Science

The K -sign depth ( K -depth) of a model parameter θ in a data set is the relative number of K -tuples among its residual vector that have alternating signs. The K -depth test based on K -depth, recently proposed by Leckey et al. (2020), is equivalent to the classical residual-based sign test for K = 2 , but is much more powerful for K ≥ 3 . This test has two major drawbacks. First, the computation of the K -depth is fairly time consuming having a polynomial time complexity of degree K , and second, the test requires knowledge about the quantiles of the test statistic which previously had to be obtained by simulation for each sample size individually. We tackle both of these drawbacks by presenting a limit theorem for the distribution of the test statistic and deriving an (asymptotically equivalent) form of the K -depth which can be computed efficiently. For K = 3 , such a limit theorem was already derived in Kustosz et al. (2016a) by mimicking the proof for U -statistics. We provide here a much shorter proof based on Donsker’s theorem and extend it to any K ≥ 3 . As part of the proof, we derive an asymptotically equivalent form of the K-depth which can be computed in linear time. This alternative and the original implementation of the K-depth are compared with respect to their runtimes and absolute difference.

Given a directed graph G and a pair of nodes s and t , an s - t bridge of G is an edge whose removal breaks all s - t paths of G . Similarly, an s - t articulation point of G is a node whose removal breaks all s - t paths of G . Computing the sequence of all s - t bridges of G (as well as the s - t articulation points) is a basic graph problem, solvable in linear time using the classical min-cut algorithm (Ford and Fulkerson, 1956). We show a simplified and self-contained algorithm computing all s - t bridges and s - t articulation points of G , based on a single graph traversal from s to t avoiding an arbitrary s - t path, which is interrupted at the s - t bridges. Its proof of correctness uses simple inductive arguments, making the problem an application of merely graph traversal, rather than of the more complex maximum flow problem.

We present a fast and memory-efficient algorithm for transient space–time-domain elastodynamic boundary-integral analysis. Associated data-sparse approximations and operations are named fast domain partitioning hierarchical matrices (FDP=H-matrices). The fast domain partitioning method (the FDPM) solves a known problem of hierarchical matrices (H-matrices) in compressing discretized elastodynamic kernel functions. A novel set of plane-wave approximations unites the FDPM and H-matrices in an accurate analytic manner. Memory usage is O ( N log N ) and computation time O ( N M log N ) in our algorithm for a single run with N boundary elements and M time steps. Consequent cost reduction is remarkable, considering the O ( N 2 M ) memory usage and O ( N 2 M 2 ) computational time to run the orthodox time-marching implementation. Numerical experiments verify FDP=H-matrices realize O ( N M / log N ) times smaller memory and computation time with ensuring the accuracy of integral analyses.

In this paper, we propose several algorithms for determining an optimal length tree-like refutation of linear feasibility in systems of Unit Two Variable Per Inequality (UTVPI) constraints. Given an infeasible UTVPI constraint system (UCS), a refutation certifies its infeasibility. The problem of finding refutations in a UCS finds applications in domains such as program verification and operations research. In general, there exist several types of refutations of feasibility in constraint systems. In this paper, we focus on a specific type of refutation called a tree-like refutation. Tree-like refutations are complete, in the sense that if a system of linear constraints is infeasible, then it must have a tree-like refutation. Associated with a refutation is its length, which equals the total number of constraints (accounting for the reuse of constraints) that are used to establish the infeasibility of the corresponding linear constraint system. Our goal in this paper is to find an optimal length tree-like refutation (OTLR) of an infeasible UCS. We describe two deterministic algorithms that find an OTLR of a UCS. If m is the number of constraints, n is the number of variables in the system, and k is the length of an OTLR, then our two algorithms run in O ( n 3 ⋅ log k ) time and O ( m ⋅ n ⋅ k ) time respectively. We also propose a true-biased, randomized algorithm for this problem. This algorithm runs in O ( m ⋅ n ⋅ log n ) time, and returns the length of an OTLR with probability ( 1 − 1 e ) . We extend our work to weighted UTVPI constraint systems (WUCS), where a positive weight is associated with each UTVPI constraint. The weight of a tree-like refutation is defined as the sum of the weights of the constraints used by the refutation. The problem of finding a minimum weight refutation in a WUCS is called the weighted optimal length tree-like refutation (WOTLR) problem and is known to be NP-hard. We propose a pseudo-polynomial time algorithm for the WOTLR problem and convert it into a fully polynomial time approximation scheme (FPTAS).

The t -admissibility problem aims to decide whether a graph G has a spanning tree T in which the distance between any two adjacent vertices of G is at most t . In this case, G is called t -admissible, and the smallest t for which G is t -admissible is the stretch index of G . A complementary prism of G , denoted by G G ¯ , is obtained by the union of G with its complement G ¯ and the addition of a perfect matching between corresponding vertices of G and G ¯ . One of the challenges of the t -admissibility problem is to determine 3-admissible graph classes, since the computational complexity of such a problem remains open for more than 25 years. Moreover, it is known that recognizing 4-admissible graphs is, in general, an NP -complete problem (Cai and Corneil, 1995), as well as recognizing t -admissible graphs for graphs with diameter at most t + 1 , for t ≥ 4 (Papoutsakis, 2013). We prove that any graph G , non-complete graph, can be transformed into a 4-admissible one, by obtaining G G ¯ . Furthermore, we prove that the stretch indexes of G G ¯ graphs are equal to 4, and since they have diameter at most t + 1 , we present a class for which t -admissibility is solved in polynomial time. G G graphs are the Cartesian product G × K 2 , defined by the union of two copies of G and the addition of a perfect matching between corresponding vertices of the two graphs G . Interestingly, we prove that for G G graphs, whose definition is very similar to G G ¯ ’s, t -admissibility is NP -complete. Generalizing these constructions, we prove that determining t -admissibility is NP -complete for graphs that have perfect matching.

Images captured in foggy weather conditions suffers from inevitable problems such as low contrast, blurriness and less visibility. In many computer and vision applications like surveillance, object detection, object tracking and navigation, these low-quality images cannot be used and it requires improvement in the image quality. Different algorithms have been proposed in this direction and to upgrade the quality of a foggy image. Most of the existing methods gives good quality image but with high time complexity. In this paper, a novel and effective method is proposed to remove fog from a single image. The proposed method is based on principal component analysis and modified dark channel prior. In proposed algorithm, foggy image is pre-processed using principal component analysis. This pre-processed image is further enhanced using fast global smoothening filter. Time complexity of the proposed method is much less as compared to the various existing methods and at the same time, quality is also maintained. Also, proposed algorithm does not require a large data set and specific hardware. To see the effectiveness of the proposed technique, both qualitative and quantitative analysis has been done on synthetic data set as well as on natural dataset.

We study three classical graph problems – Hamiltonian path, minimum spanning tree, and minimum perfect matching on geometric graphs induced by bichromatic (red and blue) points. These problems have been widely studied for points in the Euclidean plane, and many of them are NP -hard. In this work, we consider these problems for collinear points. We show that almost all of these problems can be solved in linear time in this setting.

Given an undirected graph G = ( V , E ) and a positive integer k ∈ 1 , … , | V | , we initiate the combinatorial study of stable sets of cardinality exactly k in G . Our aim is to instigate the polyhedral investigation of the convex hull of fixed cardinality stable sets, inspired by the rich theory on the classical structure of stable sets. We introduce a large class of valid inequalities to the natural integer programming formulation of the problem. We also present simple combinatorial relaxations based on computing maximum weighted matchings, which yield dual bounds towards finding minimum-weight fixed cardinality stable sets, and particular cases which are solvable in polynomial time.

Let G = ( V , E ) be an undirected graph, L G ∈ R V × V be the associated Laplacian matrix, and b ∈ R V be a vector. Solving the Laplacian system L G x = b has numerous applications in theoretical computer science, machine learning, and network analysis. Recently, the notion of the Laplacian operator L F : R V → 2 R V for a submodular transformation F : 2 V → R + E was introduced, which can handle undirected graphs, directed graphs, hypergraphs, and joint distributions in a unified manner. In this study, we show that the submodular Laplacian system L F ( x ) ∋ b can be solved in polynomial time. Furthermore, we prove that even when the submodular Laplacian system has no solution, we can solve its regression form in polynomial time. Finally, we discuss potential applications of submodular Laplacian systems in machine learning and network analysis.

For sparse graphs, the odd cycle polytope can be used to compute useful bounds for the maximum stable set problem quickly. Yannakakis (1991) introduced an extended formulation for the odd cycle inequalities of the stable set polytope, which provides a direct way to optimize over the odd cycle polytope in polynomial time, although there can exist exponentially many odd cycles in given graphs in general. We present another extended formulation for the odd cycle polytope that uses less variables and inequalities than Yannakakis’ formulation. Moreover, we compare the running time of both formulations as relaxations of the maximum stable set problem in a computational study.