Dead-End Elimination for Weighted CSP
Soft neighborhood substitutability (SNS) is a powerful technique to automatically detect and prune dominated solutions in combinatorial optimization. Recently, it has been shown in  that enforcing partial SNS (PSNS r ) during search can be worthwhile in the context of Weighted Constraint Satisfaction Problems (WCSP). However, for some problems, especially with large domains, PSNS r is still too costly to enforce due to its worst-case time complexity in O(ned 4) for binary WCSP. We present a simplified dominance breaking constraint, called restricted dead-end elimination (DEE r ), the worst-case time complexity of which is in O(ned 2). Dead-end elimination was introduced in the context of computational biology as a preprocessing technique to reduce the search space [13, 14, 16, 17, 28, 30]. Our restriction involves testing only one pair of values per variable instead of all the pairs, with the possibility to prune several values at the same time. We further improve the original dead-end elimination criterion, keeping the same time and space complexity as DEE r . Our results show that maintaining DEE r during a depth-first branch and bound (DFBB) search is often faster than maintaining PSNS r and always faster than or similar to DFBB alone.
Keywordscombinatorial optimization dominance rule weighted constraint satisfaction problem soft neighborhood substitutability
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- 9.Cooper, M., de Givry, S., Sanchez, M., Schiex, T., Zytnicki, M.: Virtual arc consistency for weighted CSP. In: Proc. of AAAI 2008, Chicago, IL (2008)Google Scholar
- 11.Cooper, M.C., de Givry, S., Schiex, T.: Optimal soft arc consistency. In: Proc. of IJCAI 2007, Hyderabad, India, pp. 68–73 (January 2007)Google Scholar
- 15.Freuder, E.C.: Eliminating interchangeable values in constraint satisfaction problems. In: Proc. of AAAI 1991, Anaheim, CA, pp. 227–233 (1991)Google Scholar
- 16.Georgiev, I., Lilien, R., Donald, B.: Improved pruning algorithms and divide-and-conquer strategies for dead-end elimination, with application to protein design. Bioinformatics 22(14), e174–e183 (2006)Google Scholar
- 18.Harvey, W.D., Ginsberg, M.L.: Limited discrepency search. In: Proc. of the 14th IJCAI, Montréal, Canada (1995)Google Scholar
- 20.Koster, A.M.C.A.: Frequency assignment: Models and Algorithms. Ph.D. thesis, University of Maastricht, The Netherlands (November 1999), www.zib.de/koster/thesis.html
- 21.Larrosa, J.: On arc and node consistency in weighted CSP. In: Proc. AAAI 2002, Edmondton (CA), pp. 48–53 (2002)Google Scholar
- 22.Larrosa, J., de Givry, S., Heras, F., Zytnicki, M.: Existential arc consistency: getting closer to full arc consistency in weighted CSPs. In: Proc. of the 19th IJCAI, Edinburgh, Scotland, pp. 84–89 (August 2005)Google Scholar
- 27.Leyton-Brown, K., Pearson, M., Shoham, Y.: Towards a Universal Test Suite for Combinatorial Auction Algorithms. In: ACM E-Commerce, pp. 66–76 (2000)Google Scholar