Minimum Weight Vertex Cover Research Articles

Cooperative mission planning based on game theory for UAVs and USVs heterogeneous system in dynamic scenario

PurposeThe purpose of this paper is to present and implement a task allocation method based on game theory for reconnaissance mission planning of UAVs and USVs system.Design/methodology/approachIn this paper, the decision-making framework via game theory of mission planning is constructed. The mission planning of UAVs–USVs is transformed into a potential game optimization problem by introducing a minimum weight vertex cover model. The modified population-based game-theoretic optimizer (MPGTO) is used to improve the efficiency of solving this complex multi-constraint assignment problem.FindingsSeveral simulations are carried out to exhibit that the proposed algorithm obtains the superiority on quality and efficiency of mission planning solutions to some existing approaches.Research limitations/implicationsSeveral simulations are carried out to exhibit that the proposed algorithm obtains the superiority on quality and efficiency of mission planning solutions to some existing approaches.Practical implicationsThe proposed framework and algorithm are expected to be applied to complex real scenarios with uncertain targets and heterogeneity.Originality/valueThe decision framework via game theory is proposed for the mission planning problem of UAVs–USVs and a MPGTO with swarm evolution, and the adaptive iteration mechanism is presented for ensuring the efficiency and quality of the solution.

Minimum Weighted Vertex Cover on Different Graphs and It's Algorithm

Minimum Weighted Vertex Cover on Different Graphs and It's Algorithm

Constraint Composite Graph-Based Weighted CSP Solvers: An Empirical Study

The Weighted Constraint Satisfaction Problem (WCSP) is a very expressive framework for optimization problems. The Constraint Composite Graph (CCG) is a graphical representation of a given (Boolean) WCSP that facilitates its reduction to a Minimum Weighted Vertex Cover (MWVC) problem by introducing intelligently chosen auxiliary variables. It also enables kernelization: a maxflow procedure used to fix the optimal values of a subset of the variables before initiating search. In this paper, we present some CCG-based WCSP solvers and compare their performance against toulbar2, a state-of-the-art WCSP solver, on a variety of benchmark instances. We also study the effectiveness of kernelization.

Ising Hamiltonians for Constrained Combinatorial Optimization Problems and the Metropolis‐Hastings Warm‐Starting Algorithm

AbstractQuantum approximate optimization algorithm (QAOA) is a promising variational quantum algorithm for combinatorial optimization problems. However, the implementation of QAOA is limited due to the requirement that the problems be mapped to Ising Hamiltonians and the nonconvex optimization landscapes. Although the Ising Hamiltonians for many NP hard problems have been obtained, a general method to obtain the Ising Hamiltonians for constrained combinatorial optimization problems (CCOPs) has not yet been investigated. In this paper, a general method is introduced to obtain the Ising Hamiltonians for CCOPs and the Metropolis‐Hastings warm‐starting algorithm for QAOA is presented which can provably converge to the global optimal solutions. The effectiveness of this method is demonstrated by tackling the minimum weight vertex cover (MWVC) problem, the minimum vertex cover (MVC) problem, and the maximal independent set problem as examples. The Ising Hamiltonian for the MWVC problem is obtained first time by using this method. The advantages of the Metropolis‐Hastings warm‐starting algorithm presented here is numerically analyzed through solving 30 randomly generated MVC cases with 1‐depth QAOA.

An evolutionary game algorithm for minimum weighted vertex cover problem

An evolutionary game algorithm for minimum weighted vertex cover problem

A Maximum Degree related Condition to Asymmetric Game in Weighted Vertex Cover Networks

Minimum weighted vertex cover (MWVC) is an important optimization problem in the application of complex network theory, and the asymmetric game model sheds light on the essential mechanism of the MWVC. In this paper, a new condition for the effectiveness of the asymmetric game is discovered based on the imbalance of weighted networks. When the new condition satisfies, a Nash equilibrium (NE) becomes a bridge state between vertex cover (VC) state and MWVC state, and any initial state of the network can reach the NE following the feedback-based best response (FBR) algorithm. Numerical experiments verify that this new condition has stronger stability and wider range of applications than the original one. FBR algorithm with the new condition shows superiority over other distributed algorithms. We also qualitatively clarify the network property factors affecting the performance of MWVC to some extent.

Better Approximation for Distributed Weighted Vertex Cover via Game-Theoretic Learning

Toward better approximation for the minimum-weighted vertex cover (MWVC) problem in multiagent systems, we present a distributed algorithm from the perspective of learning in games. For self-organized coordination and optimization, we see each vertex as a potential game player who makes decisions using local information of its own and the immediate neighbors. The resulting Nash equilibrium is classified into two categories, i.e., the inferior Nash equilibrium (INE) and the dominant Nash equilibrium (DNE). We show that the optimal solution must be a DNE. To achieve better approximation ratios, local rules of perturbation and weighted memory are designed, with the former destroying the stability of an INE and the latter facilitating the refinement of a DNE. By showing the existence of an improvement path from any INE to a DNE, we prove that when the memory length is larger than 1, our algorithm converges in finite time to DNEs, which could not be improved by exchanging the action of a selected node with all its unselected neighbors. Moreover, additional freedom for solution efficiency refinement is provided by increasing the memory length. Finally, intensive comparison experiments demonstrate the superiority of the presented methodology to the state of the art, both in solution efficiency and computation speed.

Fixed set search applied to the multi-objective minimum weighted vertex cover problem

The Fixed Set Search (FSS) is a novel metaheuristic that adds a learning mechanism to the Greedy Randomized Adaptive Search Procedure (GRASP). In recent publications, its efficiency has been shown on different types of combinatorial optimization problems like routing, machine scheduling and covering. In this paper the FSS is adapted to multi-objective problems for finding Pareto Front approximations. This adaptation is illustrated for the bi-objective Minimum Weighted Vertex Cover Problem (MWVCP). In this work, a simple and effective bi-objective GRASP algorithm for the MWVCP is developed in the first stage. One important characteristic of the proposed GRASP is that it avoids the use of weighted sums of objective functions in the local search and the greedy algorithm. In the second stage, the bi-objective GRASP is extended to the FSS by adding a learning mechanism adapted to multi-objective problems. The conducted computational experiments show that the proposed FSS and GRASP algorithm significantly outperforms existing methods for the bi-objective MWVCP. To fully evaluate the learning mechanism of the FSS, it is compared to the underlying GRASP algorithm on a wide range of performance indicators related to convergence, distribution, spread and cardinality.

Approximating the discrete time-cost tradeoff problem with bounded depth

We revisit the deadline version of the discrete time-cost tradeoff problem for the special case of bounded depth. Such instances occur for example in VLSI design. The depth of an instance is the number of jobs in a longest chain and is denoted by d. We prove new upper and lower bounds on the approximability. First we observe that the problem can be regarded as a special case of finding a minimum-weight vertex cover in a d-partite hypergraph. Next, we study the natural LP relaxation, which can be solved in polynomial time for fixed d and—for time-cost tradeoff instances—up to an arbitrarily small error in general. Improving on prior work of Lovász and of Aharoni, Holzman and Krivelevich, we describe a deterministic algorithm with approximation ratio slightly less than frac{d}{2} for minimum-weight vertex cover in d-partite hypergraphs for fixed d and given d-partition. This is tight and yields also a frac{d}{2}-approximation algorithm for general time-cost tradeoff instances, even if d is not fixed. We also study the inapproximability and show that no better approximation ratio than frac{d+2}{4} is possible, assuming the Unique Games Conjecture and text {P}ne text {NP}. This strengthens a result of Svensson [21], who showed that under the same assumptions no constant-factor approximation algorithm exists for general time-cost tradeoff instances (of unbounded depth). Previously, only APX-hardness was known for bounded depth.

A population-based game-theoretic optimizer for the minimum weighted vertex cover

Toward higher solution efficiency and faster computation, this paper addresses the minimum weighted vertex cover (MWVC) problem by introducing game theory into iterated optimization and proposing a population-based game-theoretic optimizer (PGTO). A group of candidate solutions are iterated through the specially designed procedures of swarm evolution (SE), learning in games (LIG), and local search (LS) successively. Within the framework of potential game theory, we prove that LIG computes in finite time Nash equilibria that represent vertex cover solutions where no redundant nodes exist. Moreover, theoretical analysis is presented that by exchanging the actions of certain neighbours, LS is capable of generating better results upon the input Nash equilibrium. Through intensive numerical experiments, we show that while enlarging the population size could boost the global objective, a mutation probability between 0.05 and 0.2 is more likely to provide the best performance. Comparison experiments against the state of the art demonstrate the superiority of the presented methodology, both in terms of solution quality and computation speed.

Optimal distributed covering algorithms

We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank f. This problem is equivalent to the Minimum Weight Set Cover problem in which the frequency of every element is bounded by f. The approximation factor of our algorithm is (f+varepsilon ). Let varDelta denote the maximum degree in the hypergraph. Our algorithm runs in the congest model and requires O(log {varDelta } / log log varDelta ) rounds, for constants varepsilon in (0,1] and fin {mathbb {N}}^+. This is the first distributed algorithm for this problem whose running time does not depend on the vertex weights nor the number of vertices. Thus adding another member to the exclusive family of provably optimal distributed algorithms. For constant values of f and varepsilon , our algorithm improves over the (f+varepsilon )-approximation algorithm of Kuhn et al. (SODA, 2006)whose running time is O(log varDelta + log W), where W is the ratio between the largest and smallest vertex weights in the graph. Our algorithm also achieves an f-approximation for the problem in O(flog n) rounds, improving over the classical result of Khuller et al. (J Algorithms, 1994) that achieves a running time of O(flog ^2 n). Finally, for weighted vertex cover (f=2) our algorithm achieves a deterministic running time of O(log n), matching the randomized previously best result of Koufogiannakis and Young (Distrib Comput, 2011). We also show that integer covering-programs can be reduced to the Minimum Weight Set Cover problem in the distributed setting. This allows us to achieve an (flceil log _2(M)+1 rceil +varepsilon )-approximate integral solution in O(1+f/logn)·logΔloglogΔ+(f·logM)1.01·logε-1·(logΔ)0.01\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} O\\left( (1+f/\\log n)\\cdot \\left( {\\frac{\\log \\varDelta }{ \\log \\log \\varDelta } + ({f\\cdot \\log M})^{1.01}\\cdot \\log \\varepsilon ^{-1}\\cdot (\\log \\varDelta )^{0.01}}\\right) \\right) \\end{aligned}$$\\end{document}rounds, where f bounds the number of variables in a constraint, varDelta bounds the number of constraints a variable appears in, and M=max left{ 1, lceil 1/a_{min } rceil right} , where a_{min } is the smallest normalized constraint coefficient.

Jumping particle swarm optimisation method for solving minimum weight vertex cover problem

Jumping particle swarm optimisation method for solving minimum weight vertex cover problem

Jumping particle swarm optimisation method for solving minimum weight vertex cover problem

The minimum weight vertex cover problem (MWVCP) is one of the classic combinatorial optimisation problems. In this paper, we have proposed a modified jumping particle swarm optimisation approach, n...

A Fast and Robust Heuristic Algorithm for the Minimum Weight Vertex Cover Problem

The minimum weight vertex cover problem (MWVCP) is a fundamental combinatorial optimization problem with various real-world applications. The MWVCP seeks a vertex cover of an undirected graph such that the sum of the weights of the selected vertices is as small as possible. In this paper, we present an effective algorithm to solve the MWVCP. First, a master-apprentice evolutionary algorithm based on two individuals is conducted to enhance the diversity of solutions. Second, a hybrid tabu search combined configuration checking and solution-based tabu search is introduced to intensify local search procedure. Harnessing the power of the evolutionary strategy and a novel variant of hybrid tabu search, Master-Apprentice Evolutionary Algorithm with Hybrid Tabu Search, MAE-HTS, is presented. Results of extensive computational experiments using standard benchmark instances and other large-scale instances demonstrate the efficacy of our algorithm in terms of solution quality, running time, and robustness compared to state-of-the-art heuristics from the literature and the commercial MIP solver Gurobi. We also systematically analyze the role of each individual component of the algorithm which when worked in unison produced superior outcomes. In particular, MAE-HTS produced improved solutions for 2 out of 126 public benchmark instances with better running time. In addition, our MAE-HTS outperforms other state-of-the-art algorithms DLSWCC and NuMWVC for 72 large scale MWVCP instances by obtaining the best results for 64 ones, while other two reference algorithms can only obtain 27 best results at most.

Optimized Energy – Efficient Path Planning Strategy in WSN With Multiple Mobile Sinks

Recently, wireless sensor networks (WSNs) were perceived as the foundation infrastructure that paved the way to the emergence of the Internet of Things (IoT). However, a challenging issue exists when WSNs are integrated into the IoT because of high energy consumption in their nodes and poor network lifespan. Therefore, the elementary discussions in WSN are energy scarcity in sensor nodes, sensors' data exchange, and routing protocols. To address the aforesaid shortcomings, this paper develops an optimized energy-efficient path planning strategy that prolongs the network lifetime and enhances its connectivity. The proposed approach has four successive procedures: initially, the sensing field is partitioned into equal regions depending on the number of deployed mobile sinks that eliminate the energy-hole problem. A new heuristic clustering approach called stable election algorithm (SEA) is introduced to minimize the message exchange between sensor nodes and prevent frequent cluster heads rotation. A sojourn location determination algorithm is proposed based on the minimum weighted vertex cover problem (MWVCP) to find the best position for the sinks to stop and collect the data from cluster heads. Finally, three optimization techniques are utilized to evaluate the optimized mobile sinks' trajectories using multi-objective evolutionary algorithms (MOEAs). Whilst the performance of the developed work was evaluated in terms of cluster heads number, network lifetime, the execution time of the sinks' sojourn locations determination algorithm, the convergence rate of optimization techniques, and data delivery. The simulation scenarios conducted in MATLAB and the obtained results showed that the introduced approach outperformed comparable existing schemes. It succeeded in prolonging the network lifetime up to 66% compared to existing routing protocols.

Risk-Aware Identification of Highly Suspected COVID-19 Cases in Social IoT: A Joint Graph Theory and Reinforcement Learning Approach.

The recent outbreak of the coronavirus disease 2019 (COVID-19) has rapidly become a pandemic, which calls for prompt action in identifying suspected cases at an early stage through risk prediction. To suppress its further spread, we exploit the social relationships between mobile devices in the Social Internet of Things (SIoT) to help control its propagation by allocating the limited protective resources to the influential so-called high-degree individuals to stem the tide of precipitated spreading. By exploiting the so-called differential contact intensity and the infectious rate in susceptible-exposed-infected-removed (SEIR) epidemic model, the resultant optimization problem can be transformed into the minimum weight vertex cover (MWVC) problem of graph theory. To solve this problem in a high-dynamic random network topology, we propose an adaptive scheme by relying on the graph embedding technique during the state representation and reinforcement learning in the training phase. By relying on a pair of real-life datasets, the results demonstrate that our scheme can beneficially reduce the epidemiological reproduction rate of the infection. This technique has the potential of assisting in the early identification of COVID-19 cases.

Multi-Objective Neighborhood Search Algorithm Based on Decomposition for Multi-Objective Minimum Weighted Vertex Cover Problem

The multi-objective minimum weighted vertex cover problem aims to minimize the sum of different single type weights simultaneously. In this paper, we focus on the bi-objective minimum weighted vertex cover and propose a multi-objective algorithm integrating iterated neighborhood search with decomposition technique to solve this problem. Initially, we adopt the decomposition method to divide the multi-objective problem into several scalar optimization sub-problems. Meanwhile, to find more possible optimal solutions, we design a mixed score function according to the problem feature, which is applied in initializing procedure and neighborhood search. During the neighborhood search, three operators ( A d d , D e l e t e , S w a p ) explore the search space effectively. We performed numerical experiments on many instances, and the results show the effectiveness of our new algorithm (combining decomposition and neighborhood search with mixed score) on several experimental metrics. We compared our experimental results with the classical multi-objective algorithm non-dominated sorting genetic algorithm II. It was obviously shown that our algorithm can provide much better results than the comparative algorithm considering the different metrics.

NuMWVC: A novel local search for minimum weighted vertex cover problem

The problem of finding a minimum weighted vertex cover (MWVC) in a graph is a well-known combinatorial optimisation problem with important applications. This article introduces a novel local search algorithm called NuMWVC for MWVC based on three ideas. First, four reduction rules are introduced during the initial construction phase. Second, a strategy called configuration checking with aspiration, which aims for reducing cycling in local search, is proposed for MWVC for the first time. Moreover, a self-adaptive vertex removing strategy is proposed to save time spent on searching solutions for which the quality is likely far from optimality. Experimental results show that NuMWVC outperforms state-of-the-art local search algorithms for MWVC on the standard benchmarks, massive graphs and real-world problem (map labeling problem) instances.

A multi-start iterated greedy algorithm for the minimum weight vertex cover P3 problem

Given a vertex-weighted graph G=(V,E) and a positive integer k ≥ 2, the minimum weight vertex cover Pk (MWVCPk) problem is to find a vertex subset F ⊆ V with minimum total weight such that every path of order k in G contains at least one vertex in F. For any integer k ≥ 2, the MWVCPk problem for general graphs is NP-hard. In this paper, we restrict our attention to the MWVCP3 problem and present a multi-start iterated greedy algorithm to solve the MWVCP3 problem. The experiments are carried out on randomly generated instances with up to 1000 vertices and 250000 edges. Our work is the first one to adopt heuristic algorithms to solve the MWVCP3 problem, and the experimental results show that our algorithm performs reasonably well in practice.

Towards faster local search for minimum weight vertex cover on massive graphs

The minimum weight vertex cover (MWVC) problem is a well known NP-hard problem with various real-world applications. In this paper, we design an efficient algorithm named FastWVC to solve MWVC problem in massive graphs. To this end, we propose a construction procedure, which aims to generate a quality initial vertex cover in short time. We also propose a new exchange step for reconstructing a vertex cover. Additionally, a cost-effective strategy is used for choosing adding vertices, which can accelerate the algorithm. Experiments on 102 instances were conducted to confirm the effectiveness of our algorithm. The results show that the FastWVC algorithm outperforms other algorithms in terms of both solution quality and computational time in most of the instances. We also carry out experiments that analyze the effectiveness of the underlying ideas.