Exploiting decomposition on constraint problems with high tree-width

  • Authors:

  • Matthew Kitching;Fahiem Bacchus

  • Affiliations:

  • Department of Computer Science, University of Toronto, Canada;Department of Computer Science, University of Toronto, Canada

  • Venue:
  • IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
  • Year:
  • 2009

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Abstract

Decomposition is an effective technique for solving discrete Constraint Optimization Problems (COPs) with low tree-width. On problems with high tree-width, however, existing decomposition algorithms offer little advantage over branch and bound search (B&B). In this paper we propose a method for exploiting decomposition on problems with high treewidth. Our technique involves modifying B&B to detect and exploit decomposition on a selected subset of the problem's objectives. Decompositions over this subset, generated during search, are exploited to compute tighter bounds allowing B&B to prune more of its search space. We present a heuristic for selecting an appropriate subset of objectives--one that readily decomposes during search and yet can still provide good bounds. We demonstrate empirically that our approach can significantly improve B&B's performance and outperform standard decomposition algorithms on a variety of high tree-width problems.