The p-center problem consists of choosing a subset of vertices in an undirected graph as facilities in order to minimize the maximum distance between a client and its closest facility. This paper presents a greedy ran...The p-center problem consists of choosing a subset of vertices in an undirected graph as facilities in order to minimize the maximum distance between a client and its closest facility. This paper presents a greedy randomized adaptive search procedure with path-relinking （GRASP/PR） algorithm for the p-center problem, which combines both GRASP and path-relinking. Each iteration of GRASP/PR consists of the construction of a randomized greedy solution, followed by a tabu search procedure. The resulting solution is combined with one of the elite solutions by path-relinking, which consists in exploring trajectories that connect high-quality solutions. Experiments show that GRASP/PR is competitive with the state-of-the-art algorithms in the literature in terms of both solution quality and computational efficiency. Specifically, it virtually improves the previous best known results for 10 out of 40 large instances while matching the best known results for others.展开更多
The biggest bottleneck in DNA computing is exponential explosion, in which the DNA molecules used as data in information processing grow exponentially with an increase of problem size. To overcome this bottleneck and ...The biggest bottleneck in DNA computing is exponential explosion, in which the DNA molecules used as data in information processing grow exponentially with an increase of problem size. To overcome this bottleneck and improve the processing speed, we propose a DNA computing model to solve the graph vertex coloring problem. The main points of the model are as follows： The exponential explosion prob- lem is solved by dividing subgraphs, reducing the vertex colors without losing the solutions, and ordering the vertices in subgraphs; and the bio-operation times are reduced considerably by a designed parallel polymerase chain reaction （PCR） technology that dramatically improves the processing speed. In this arti- cle, a 3-colorable graph with 61 vertices is used to illustrate the capability of the DNA computing model. The experiment showed that not only are all the solutions of the graph found, but also more than 99% of false solutions are deleted when the initial solution space is constructed. The powerful computational capability of the model was based on specific reactions among the large number of nanoscale oligonu- cleotide strands. All these tiny strands are operated by DNA self-assembly and parallel PCR. After thou- sands of accurate PCR operations, the solutions were found by recognizing, splicing, and assembling. We also prove that the searching capability of this model is up to 0（3^59）. By means of an exhaustive search, it would take more than 896 000 years for an electronic computer （5 x 10^14 s-1） to achieve this enormous task. This searching capability is the largest among both the electronic and non-electronic computers that have been developed since the DNA computing model was proposed by Adleman＇s research group in 2002 （with a searching capability of 0（2^20））.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
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
基金The research was supported by the National Natural Science Foundation of China under Grant Nos. 61370183 and 61262011.
文摘The p-center problem consists of choosing a subset of vertices in an undirected graph as facilities in order to minimize the maximum distance between a client and its closest facility. This paper presents a greedy randomized adaptive search procedure with path-relinking （GRASP/PR） algorithm for the p-center problem, which combines both GRASP and path-relinking. Each iteration of GRASP/PR consists of the construction of a randomized greedy solution, followed by a tabu search procedure. The resulting solution is combined with one of the elite solutions by path-relinking, which consists in exploring trajectories that connect high-quality solutions. Experiments show that GRASP/PR is competitive with the state-of-the-art algorithms in the literature in terms of both solution quality and computational efficiency. Specifically, it virtually improves the previous best known results for 10 out of 40 large instances while matching the best known results for others.
基金The authors are grateful for the support from the National Natural Science Foundation of China （61632002, 61379059, and 61572046）.
文摘The biggest bottleneck in DNA computing is exponential explosion, in which the DNA molecules used as data in information processing grow exponentially with an increase of problem size. To overcome this bottleneck and improve the processing speed, we propose a DNA computing model to solve the graph vertex coloring problem. The main points of the model are as follows： The exponential explosion prob- lem is solved by dividing subgraphs, reducing the vertex colors without losing the solutions, and ordering the vertices in subgraphs; and the bio-operation times are reduced considerably by a designed parallel polymerase chain reaction （PCR） technology that dramatically improves the processing speed. In this arti- cle, a 3-colorable graph with 61 vertices is used to illustrate the capability of the DNA computing model. The experiment showed that not only are all the solutions of the graph found, but also more than 99% of false solutions are deleted when the initial solution space is constructed. The powerful computational capability of the model was based on specific reactions among the large number of nanoscale oligonu- cleotide strands. All these tiny strands are operated by DNA self-assembly and parallel PCR. After thou- sands of accurate PCR operations, the solutions were found by recognizing, splicing, and assembling. We also prove that the searching capability of this model is up to 0（3^59）. By means of an exhaustive search, it would take more than 896 000 years for an electronic computer （5 x 10^14 s-1） to achieve this enormous task. This searching capability is the largest among both the electronic and non-electronic computers that have been developed since the DNA computing model was proposed by Adleman＇s research group in 2002 （with a searching capability of 0（2^20））.
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.
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.
