Abstract
We introduce a novel stochastic local search algorithm for the vertex cover problem. Compared to current exhaustive search techniques, our algorithm achieves excellent performance on a suite of problems drawn from the field of biology. We also evaluate our performance on the commonly used DIMACS benchmarks for the related clique problem, finding that our approach is competitive with the current best stochastic local search algorithm for finding cliques. On three very large problem instances, our algorithm establishes new records in solution quality.
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Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company (1979)
Gomes, F.C., Meneses, C.N., Pardalos, P.M., Viana, G.V.R.: Experimental analysis of approximation algorithms for the vertex cover and set covering problems. Computers and Operations Research 33(12), 3520–3534 (2006)
Abu-Khzam, F.N., Langston, M.A., Shanbhag, P., Symons, C.T.: Scalable parallel algorithms for FPT problems. Algorithmica 45, 269–284 (2006)
Evans, I.K.: Evolutionary algorithms for vertex cover. In: Porto, V.W., Waagen, D. (eds.) Evolutionary Programming VII. LNCS, vol. 1447, pp. 377–386. Springer, Heidelberg (1998)
Gilmour, S., Dras, M.: Kernelization as heuristic structure for the vertex cover problem. In: Hess, F., Pauli, S., Pohst, M. (eds.) Algorithmic Number Theory. LNCS, vol. 4076, Springer, Heidelberg (2006)
Downey, R.G., Fellows, M.R., Stege, U.: Parameterized complexity: A framework for systematically confronting computational intractability. In: Contemporary Trends in Discrete Mathematics: From DIMACS and DIMATIA to the Future. DIMACS Series, vol. 49, pp. 49–99 (1999)
Xu, K.: BHOSLIB: Benchmarks with hidden optimum solutions for graph problems (maximum clique, maximum independent set, minimum vertex cover and vertex coloring) – hiding exact solutions in random graphs. Web site, http://www.nlsde.buaa.edu.cn/~kexu/benchmarks/graph-benchmarks.htm
Niedermeier, R., Rossmanith, P.: Upper bounds for vertex cover further improved. In: STACS 1999. Proceedings of the 16th Symposium on Theoretical Aspects in Computer Science, pp. 561–570 (1999)
Cheetham, J., Dehne, F., Rau-Chaplin, A., Stege, U., Taillon, P.J.: Solving large FPT problems on coarse grained parallel machines. Journal of Computer and System Sciences 67, 691–706 (2003)
Shyu, S.J., Yin, P.Y., Lin, B.M.T.: An ant colony optimization algorithm for the minimum weight vertex cover problem. Annals of Operations Research 131(1–4), 283–304 (2004)
Johnson, D.S., Trick, M.A. (eds.): Cliques, Coloring and Satisfiability: Second DIMACS Implementation Challenge. DIMACS Series, vol. 26. American Mathematical Society (1996)
Barbosa, V.C., Campos, L.C.D.: A novel evolutionary formulation of the maximum independent set problem. Journal of Combinatorial Optimization 8, 419–437 (2004)
Busygin, S., Butenko, S., Pardalos, P.M.: A heuristic for the maximum independent set problem based on optimization of a quadratic over a sphere. Journal of Combinatorial Optimization 6, 287–297 (2002)
Pullan, W., Hoos, H.H.: Dynamic local search for the maximum clique problem. Journal of Artificial Intelligence Research 25, 159–185 (2006)
Pullan, W.: Phased local search for the maximum clique problem. Journal of Combinatorial Optimization 12, 303–323 (2006)
Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Morgan Kaufmann, San Francisco (2004)
Kullmann, O.: The SAT 2005 solver competition on random instances. Journal on Satisfiability, Boolean Modeling and Computation 2, 61–102 (2005)
Selman, B., Kautz, H.A.: Domain-independent extensions to GSAT: Solving large structured satisfiability problems. In: IJCAI 1993. Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, pp. 290–295 (1993)
Thornton, J., Pham, D.N., Bain, S., Ferreira Jr., V.: Additive versus multiplicative clause weighting for SAT. In: AAAI 2004. Proceedings of the Nineteenth National Conference on Artificial Intelligence, pp. 191–196 (2004)
Xu, K., Boussemart, F., Hemery, F., Lecoutre, C.: A simple model to generate hard satisfiable instances. In: IJCAI 2005. Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, pp. 337–342 (2005)
Le Berre, D., Simon, L.: The SAT 2004 competition. Web site, http://www.lri.fr/~simon/contest04/results/
Liu, L., Truszczynski, M.: Local-search techniques for propositional logic extended with cardinality constraints. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 495–509. Springer, Heidelberg (2003)
Brockington, M., Culberson, J.C.: Camouflaging independent sets in quasi-random graphs, pp. 75–88 [11]
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Richter, S., Helmert, M., Gretton, C. (2007). A Stochastic Local Search Approach to Vertex Cover. In: Hertzberg, J., Beetz, M., Englert, R. (eds) KI 2007: Advances in Artificial Intelligence. KI 2007. Lecture Notes in Computer Science(), vol 4667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74565-5_31
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DOI: https://doi.org/10.1007/978-3-540-74565-5_31
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