---
title: "Exploiting Decomposition on Constraint Problems with High Tree-Width"
authors:
  - "Matthew Kitching"
  - "Fahiem Bacchus"
doi: ""
url: "https://ijcai.org/proceedings/2009/94"
pdf: "https://ijcai.org/proceedings/2009/0094.pdf"
venue: "Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence"
year: 2009
pages: "525-530"
track: ""
keywords:
---

# Exploiting Decomposition on Constraint Problems with High Tree-Width

Matthew Kitching, Fahiem Bacchus

*Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence*, pages 525-530.

## Abstract

Decomposition is an effective technique for solving discrete Constraint Optimization Problems (COPs) with low tree-width. On problems with high treewidth, 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.Matthew Kitching, Fahiem Bacchus