An efficient local search for partial vertex cover problem

In this paper, an efficient local search framework, namely GRASP-PVC, is proposed to solve the minimum partial vertex cover problem. In order to speed up the convergence, a novel least-cost vertex selecting strategy is applied into GRASP-PVC. As far as we know, no heuristic algorithms have ever been reported to solve this momentous problem and we compare GRASP-PVC with a commercial integer programming solver CPLEX as well as a 2-approximation algorithm on two standard benchmark libraries called DIMACS and BHOSLIB. Experimental results evince that GRASP-PVC finds much better partial vertex covers than CPLEX and the approximation algorithm on most instances. Additional experimental results also confirm the validity of the least-cost vertex selecting strategy.

[1]  Valmir Carneiro Barbosa,et al.  A Novel Evolutionary Formulation of the Maximum Independent Set Problem , 2003, J. Comb. Optim..

[2]  Minghao Yin,et al.  Animal migration optimization: an optimization algorithm inspired by animal migration behavior , 2014, Neural Computing and Applications.

[3]  Jianan Wang,et al.  Two Local Search Algorithms for Partition Vertex Cover Problem , 2016 .

[4]  M. Trick,et al.  Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, Workshop, October 11-13, 1993 , 1996 .

[5]  Michael Kearns,et al.  Computational complexity of machine learning , 1990, ACM distinguished dissertations.

[6]  Dorit S. Hochbaum,et al.  The t-Vertex Cover Problem: Extending the Half Integrality Framework with Budget Constraints , 1998, APPROX.

[7]  Xingming Sun,et al.  Achieving Efficient Cloud Search Services: Multi-Keyword Ranked Search over Encrypted Cloud Data Supporting Parallel Computing , 2015, IEICE Trans. Commun..

[8]  Xiangtao Li,et al.  Self-adaptive constrained artificial bee colony for constrained numerical optimization , 2012, Neural Computing and Applications.

[9]  Mauricio G. C. Resende,et al.  Greedy Randomized Adaptive Search Procedures , 1995, J. Glob. Optim..

[10]  Jin Wang,et al.  A Variable Threshold-Value Authentication Architecture for Wireless Mesh Networks , 2014 .

[11]  Wayne J. Pullan,et al.  Dynamic Local Search for the Maximum Clique Problem , 2011, J. Artif. Intell. Res..

[12]  Kaile Su,et al.  Two Weighting Local Search for Minimum Vertex Cover , 2015, AAAI.

[13]  Aravind Srinivasan,et al.  Improved Approximation Algorithms for the Partial Vertex Cover Problem , 2002, APPROX.

[14]  Nader H. Bshouty,et al.  Massaging a Linear Programming Solution to Give a 2-Approximation for a Generalization of the Vertex Cover Problem , 1998, STACS.

[15]  Matteo Fischetti,et al.  Modeling and Solving the Crew Rostering Problem , 1998, Oper. Res..

[16]  Xiangtao Li,et al.  Enhancing the performance of cuckoo search algorithm using orthogonal learning method , 2013, Neural Computing and Applications.

[17]  M. Resende,et al.  A probabilistic heuristic for a computationally difficult set covering problem , 1989 .

[18]  Hanif D. Sherali,et al.  An Air Force Crew Allocation and Scheduling Problem , 1984 .

[19]  Charu C. Aggarwal,et al.  Optimized Crossover for the Independent Set Problem , 1997, Oper. Res..

[20]  Rajiv Gandhi,et al.  Approximation algorithms for partial covering problems , 2004, J. Algorithms.

[21]  Reuven Bar-Yehuda,et al.  Using homogenous weights for approximating the partial cover problem , 2001, SODA '99.

[22]  Minghao Yin,et al.  Two Efficient Local Search Algorithms for Maximum Weight Clique Problem , 2016, AAAI.

[23]  David S. Johnson,et al.  Cliques, Coloring, and Satisfiability , 1996 .

[24]  Erik D. Demaine,et al.  Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs , 2005, JACM.

[25]  Vasek Chvátal,et al.  A Greedy Heuristic for the Set-Covering Problem , 1979, Math. Oper. Res..

[26]  Minghao Yin,et al.  A local search algorithm with tabu strategy and perturbation mechanism for generalized vertex cover problem , 2017, Neural Computing and Applications.

[27]  Markus Bläser,et al.  Computing small partial coverings , 2003, Inf. Process. Lett..

[28]  Minghao Yin,et al.  A path cost-based GRASP for minimum independent dominating set problem , 2017, Neural Computing and Applications.

[29]  Francis J. Vasko,et al.  An application combining set covering and fuzzy sets to optimally assign metallurgical grades to customer orders , 1993 .

[30]  Samir Khuller,et al.  Algorithms for facility location problems with outliers , 2001, SODA '01.

[31]  Minghao Yin,et al.  Hybrid differential evolution and gravitation search algorithm for unconstrained optimization , 2011 .

[32]  Ke Xu,et al.  Random constraint satisfaction: Easy generation of hard (satisfiable) instances , 2007, Artif. Intell..

[33]  Robert B. Allan,et al.  On domination and independent domination numbers of a graph , 1978, Discret. Math..

[34]  Diogo Vieira Andrade,et al.  Fast local search for the maximum independent set problem , 2012, J. Heuristics.

[35]  Erik D. Demaine,et al.  Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs , 2005, TALG.

[36]  Minghao Yin,et al.  A novel local search for unicost set covering problem using hyperedge configuration checking and weight diversity , 2017, Science China Information Sciences.