A backtracking-based algorithm for hypertree decomposition

Abstract

Hypertree decompositions of hypergraphs are a generalization of tree decompositions of graphs. The corresponding hypertree-width is a measure for the acyclicity and therefore an indicator for the tractability of the associated computation problem. Several NP-hard decision and computation problems are known to be tractable on instances whose structure is represented by hypergraphs of bounded hypertree-width. Roughly speaking, the smaller the hypertree-width, the faster the computation problem can be solved. In this paper, we present the new backtracking-based algorithm det- k -decomp for computing hypertree decompositions of small width. Our benchmark evaluations have shown that det- k -decomp significantly outperforms opt- k -decomp, the only exact hypertree decomposition algorithm so far. Even compared to the best heuristic algorithm, we obtained competitive results as long as the hypergraphs are sufficiently simple.