A New Solver for the Minimum Weighted Vertex Cover Problem
Given a vertex-weighted graph \(G = \langle V, E \rangle \), the minimum weighted vertex cover (MWVC) problem is to choose a subset of vertices with minimum total weight such that every edge in the graph has at least one of its endpoints chosen. While there are good solvers for the unweighted version of this NP-hard problem, the weighted version—i.e., the MWVC problem—remains understudied despite its common occurrence in many areas of AI—like combinatorial auctions, weighted constraint satisfaction, and probabilistic reasoning. In this paper, we present a new solver for the MWVC problem based on a novel reformulation to a series of SAT instances using a primal-dual approximation algorithm as a starting point. We show that our SAT-based MWVC solver (SBMS) significantly outperforms other methods.
The research at USC was supported by NSF under grant numbers 1409987 and 1319966 and a MURI under grant number N00014-09-1-1031. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the sponsoring organizations, agencies or the U.S. government.
- 1.Berkelaar, M., Eikland, K., Notebaert, P.: lp_solve 5.5 open source (mixed integer) linear programming software (2004). http://lpsolve.sourceforge.net/5.5/
- 2.Biere, A.: Lingeling, plingeling and treengeling entering the SAT competition 2013. In: Proceedings of the SAT Competition 2013. Department of Computer Science Series of Publications B, vol. B-2013-1, pp. 51–52 (2013)Google Scholar
- 4.Büttner, M., Rintanen, J.: Satisfiability planning with constraints on the number of actions. In: The Proceedings of the International Conference on Automated Planning and Scheduling, pp. 292–299 (2005)Google Scholar
- 10.Do, M.B., Benton, J., Briel, M.V.D., Kambhampati, S.: Planning with goal utility dependencies. In: Proceedings of the International Joint Conference on Artificial Intelligence, pp. 1872–1878 (2007)Google Scholar
- 13.Gurobi Optimization, I.: Gurobi optimizer reference manual (2015). http://www.gurobi.com
- 18.Kolmogorov, V.: Primal-dual algorithm for convex Markov random fields. Technical report MSR-TR-2005-117, Microsoft Research (2005)Google Scholar
- 20.Kumar, T.K.S.: Lifting techniques for weighted constraint satisfaction problems. In: Proceedings of the International Symposium on Artificial Intelligence and Mathematics (2008)Google Scholar
- 21.Li, C.M., Quan, Z.: Combining graph structure exploitation and propositional reasoning for the maximum clique problem. In: Proceedings of the IEEE International Conference on Tools with Artificial Intelligence, pp. 344–351 (2010)Google Scholar
- 22.Manquinho, V., Marques-Silva, J., Planes, J.: Algorithms for weighted boolean optimization. In: Proceedings of the International Conference on Theory and Applications of Satisfiability Testing, pp. 495–508 (2009)Google Scholar
- 23.Narodytska, N., Bacchus, F.: Maximum satisfiability using core-guided MaxSAT resolution. In: Proceedings of the AAAI Conference on Artificial Intelligence, pp. 2717–2723 (2014)Google Scholar
- 24.Nelson, B., Kumar, T.K.S.: CircuitTSAT: a solver for large instances of the disjunctive temporal problem. In: Proceedings of the International Conference on Automated Planning and Scheduling, pp. 232–239 (2008)Google Scholar
- 25.Niskanen, S., Östergård, P.R.J.: Cliquer user’s guide, version 1.0. Technical report T48, Communications Laboratory, Helsinki University of Technology, Espoo, Finland (2003)Google Scholar