Abstract
We investigate how well-performing local search algorithms for small or medium size instances can be scaled up to perform well for large inputs. We introduce a parallel kernelization technique that is motivated by the assumption that graphs in medium to large scale are composed of components which are on their own easy for state-of-the-art solvers but when hidden in large graphs are hard to solve. To show the effectiveness of our kernelization technique, we consider the well-known minimum vertex cover problem and two state-of-the-art solvers called NuMVC and FastVC. Our kernelization approach reduces an existing large problem instance significantly and produces better quality results on a wide range of benchmark instances and real world graphs.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Aarts, E., Lenstra, J.K. (eds.): Local Search in Combinatorial Optimization. Discrete Mathematics and Optimization. Wiley, Chichester (1997)
Akiba, T., Iwata, Y.: Branch-and-reduce exponential/FPT algorithms in practice: a case study of vertex cover. Theor. Comput. Sci. 609, 211–225 (2016)
Bader, D.A., Meyerhenke, H., Sanders, P., Schulz, C., Kappes, A., Wagner, D.: Benchmarking for Graph Clustering and Partitioning. In: Alhajj, R., Rokne, J. (eds.) Encyclopedia of Social Network Analysis and Mining, pp. 73–82. Springer, New York (2014)
Cai, S.: Balance between complexity and quality: local search for minimum vertex cover in massive graphs. In: Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, 25–31 July 2015, pp. 747–753 (2015)
Cai, S., Lin, J., Su, K.: Two weighting local search for minimum vertex cover. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, pp. 1107–1113 (2015)
Cai, S., Su, K., Sattar, A.: Two new local search strategies for minimum vertex cover. In: Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence (2012)
Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. TCS. Springer, London (2013)
Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Elsevier, San Francisco (2005)
Johnson, D.J., Trick, M.A. (eds.): Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, Workshop, 11–13 October 1993. American Mathematical Society, Boston (1996)
Lamm, S., Sanders, P., Schulz, C., Strash, D., Werneck, R.F.: Finding near-optimal independent sets at scale. In: Proceedings of the Eighteenth Workshop on Algorithm Engineering and Experiments, ALENEX 2016, Arlington, Virginia, USA, 10 January 2016, pp. 138–150 (2016)
Pullan, W.: Phased local search for the maximum clique problem. J. Comb. Optim. 12(3), 303–323 (2006)
Richter, S., Helmert, M., Gretton, C.: A stochastic local search approach to vertex cover. In: Hertzberg, J., Beetz, M., Englert, R. (eds.) KI 2007. LNCS (LNAI), vol. 4667, pp. 412–426. Springer, Heidelberg (2007). doi:10.1007/978-3-540-74565-5_31
Rossi, R.A., Ahmed, N.K.: The network data repository with interactive graph analytics and visualization. In: AAAI, pp. 4292–4293 (2015). http://networkrepository.com
Xu, K., Boussemart, F., Hemery, F., Lecoutre, C.: A simple model to generate hard satisfiable instances. In: Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, IJCAI 2005, pp. 337–342 (2005)
Zhang, W., Rangan, A., Looks, M.: Backbone guided local search for maximum satisfiability. In: Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence, IJCAI 2003, pp. 1179–1186 (2003)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Gao, W., Friedrich, T., Kötzing, T., Neumann, F. (2017). Scaling up Local Search for Minimum Vertex Cover in Large Graphs by Parallel Kernelization. In: Peng, W., Alahakoon, D., Li, X. (eds) AI 2017: Advances in Artificial Intelligence. AI 2017. Lecture Notes in Computer Science(), vol 10400. Springer, Cham. https://doi.org/10.1007/978-3-319-63004-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-63004-5_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-63003-8
Online ISBN: 978-3-319-63004-5
eBook Packages: Computer ScienceComputer Science (R0)