Weighted vertex cover(WVC)is one of the most important combinatorial optimization problems.In this paper,we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted n...Weighted vertex cover(WVC)is one of the most important combinatorial optimization problems.In this paper,we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted networks.We first model the WVC problem as a general game on weighted networks.Under the framework of a game,we newly define several cover states to describe the WVC problem.Moreover,we reveal the relationship among these cover states of the weighted network and the strict Nash equilibriums(SNEs)of the game.Then,we propose a game-based asynchronous algorithm(GAA),which can theoretically guarantee that all cover states of vertices converging in an SNE with polynomial time.Subsequently,we improve the GAA by adding 2-hop and 3-hop adjustment mechanisms,termed the improved game-based asynchronous algorithm(IGAA),in which we prove that it can obtain a better solution to the WVC problem than using a the GAA.Finally,numerical simulations demonstrate that the proposed IGAA can obtain a better approximate solution in promising computation time compared with the existing representative algorithms.展开更多
This paper presents a new hybrid genetic algorithm for the vertex cover problems in which scan-repair and local improvement techniques are used for local optimization. With the hybrid approach, genetic algorithms are ...This paper presents a new hybrid genetic algorithm for the vertex cover problems in which scan-repair and local improvement techniques are used for local optimization. With the hybrid approach, genetic algorithms are used to perform global exploration in a population, while neighborhood search methods are used to perform local exploitation around the chromosomes. The experimental results indicate that hybrid genetic algorithms can obtain solutions of excellent quality to the problem instances with different sizes. The pure genetic algorithms are outperformed by the neighborhood search heuristics procedures combined with genetic algorithms.展开更多
The minimum vertex cover problem(MVCP)is a well-known combinatorial optimization problem of graph theory.The MVCP is an NP(nondeterministic polynomial)complete problem and it has an exponential growing complexity with...The minimum vertex cover problem(MVCP)is a well-known combinatorial optimization problem of graph theory.The MVCP is an NP(nondeterministic polynomial)complete problem and it has an exponential growing complexity with respect to the size of a graph.No algorithm exits till date that can exactly solve the problem in a deterministic polynomial time scale.However,several algorithms are proposed that solve the problem approximately in a short polynomial time scale.Such algorithms are useful for large size graphs,for which exact solution of MVCP is impossible with current computational resources.The MVCP has a wide range of applications in the fields like bioinformatics,biochemistry,circuit design,electrical engineering,data aggregation,networking,internet traffic monitoring,pattern recognition,marketing and franchising etc.This work aims to solve the MVCP approximately by a novel graph decomposition approach.The decomposition of the graph yields a subgraph that contains edges shared by triangular edge structures.A subgraph is covered to yield a subgraph that forms one or more Hamiltonian cycles or paths.In order to reduce complexity of the algorithm a new strategy is also proposed.The reduction strategy can be used for any algorithm solving MVCP.Based on the graph decomposition and the reduction strategy,two algorithms are formulated to approximately solve the MVCP.These algorithms are tested using well known standard benchmark graphs.The key feature of the results is a good approximate error ratio and improvement in optimum vertex cover values for few graphs.展开更多
This paper describes an extremely fast polynomial time algorithm, the NOVCA （Near Optimal Vertex Cover Algorithm） that produces an optimal or near optimal vertex cover for any known undirected graph G （V, E）. NOVC...This paper describes an extremely fast polynomial time algorithm, the NOVCA （Near Optimal Vertex Cover Algorithm） that produces an optimal or near optimal vertex cover for any known undirected graph G （V, E）. NOVCA is based on the idea of（l） including the vertex having maximum degree in the vertex cover and （2） rendering the degree of a vertex to zero by including all its adjacent vertices. The three versions of algorithm, NOVCA-I, NOVCA-II, and NOVCA-random, have been developed. The results identifying bounds on the size of the minimum vertex cover as well as polynomial complexity of algorithm are given with experimental verification. Future research efforts will be directed at tuning the algorithm and providing proof for better approximation ratio with NOVCA compared to any available vertex cover algorithms.展开更多
基金partly supported by the National Natural Science Foundation of China(61751303,U20A2068,11771013)the Zhejiang Provincial Natural Science Foundation of China(LD19A010001)the Fundamental Research Funds for the Central Universities。
文摘Weighted vertex cover(WVC)is one of the most important combinatorial optimization problems.In this paper,we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted networks.We first model the WVC problem as a general game on weighted networks.Under the framework of a game,we newly define several cover states to describe the WVC problem.Moreover,we reveal the relationship among these cover states of the weighted network and the strict Nash equilibriums(SNEs)of the game.Then,we propose a game-based asynchronous algorithm(GAA),which can theoretically guarantee that all cover states of vertices converging in an SNE with polynomial time.Subsequently,we improve the GAA by adding 2-hop and 3-hop adjustment mechanisms,termed the improved game-based asynchronous algorithm(IGAA),in which we prove that it can obtain a better solution to the WVC problem than using a the GAA.Finally,numerical simulations demonstrate that the proposed IGAA can obtain a better approximate solution in promising computation time compared with the existing representative algorithms.
基金This project was supported by the National Natural Science Foundation of China the Open Project Foundation of Comput-er Software New Technique National Key Laboratory of Nanjing University.
文摘This paper presents a new hybrid genetic algorithm for the vertex cover problems in which scan-repair and local improvement techniques are used for local optimization. With the hybrid approach, genetic algorithms are used to perform global exploration in a population, while neighborhood search methods are used to perform local exploitation around the chromosomes. The experimental results indicate that hybrid genetic algorithms can obtain solutions of excellent quality to the problem instances with different sizes. The pure genetic algorithms are outperformed by the neighborhood search heuristics procedures combined with genetic algorithms.
文摘The minimum vertex cover problem(MVCP)is a well-known combinatorial optimization problem of graph theory.The MVCP is an NP(nondeterministic polynomial)complete problem and it has an exponential growing complexity with respect to the size of a graph.No algorithm exits till date that can exactly solve the problem in a deterministic polynomial time scale.However,several algorithms are proposed that solve the problem approximately in a short polynomial time scale.Such algorithms are useful for large size graphs,for which exact solution of MVCP is impossible with current computational resources.The MVCP has a wide range of applications in the fields like bioinformatics,biochemistry,circuit design,electrical engineering,data aggregation,networking,internet traffic monitoring,pattern recognition,marketing and franchising etc.This work aims to solve the MVCP approximately by a novel graph decomposition approach.The decomposition of the graph yields a subgraph that contains edges shared by triangular edge structures.A subgraph is covered to yield a subgraph that forms one or more Hamiltonian cycles or paths.In order to reduce complexity of the algorithm a new strategy is also proposed.The reduction strategy can be used for any algorithm solving MVCP.Based on the graph decomposition and the reduction strategy,two algorithms are formulated to approximately solve the MVCP.These algorithms are tested using well known standard benchmark graphs.The key feature of the results is a good approximate error ratio and improvement in optimum vertex cover values for few graphs.
文摘This paper describes an extremely fast polynomial time algorithm, the NOVCA （Near Optimal Vertex Cover Algorithm） that produces an optimal or near optimal vertex cover for any known undirected graph G （V, E）. NOVCA is based on the idea of（l） including the vertex having maximum degree in the vertex cover and （2） rendering the degree of a vertex to zero by including all its adjacent vertices. The three versions of algorithm, NOVCA-I, NOVCA-II, and NOVCA-random, have been developed. The results identifying bounds on the size of the minimum vertex cover as well as polynomial complexity of algorithm are given with experimental verification. Future research efforts will be directed at tuning the algorithm and providing proof for better approximation ratio with NOVCA compared to any available vertex cover algorithms.
