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A Backtracking-Based Algorithm for Computing Hypertree-Decompositions

Georg Gottlob·Marko Samer
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Abstract

Hypertree decompositions of hypergraphs are a generalization of tree decompositions of graphs. The corresponding hypertree-width is a measure for the cyclicity and therefore tractability of the encoded computation problem. Many NP-hard decision and computation problems are known to be tractable on instances whose structure corresponds to hypergraphs of bounded hypertree-width. Intuitively, 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 not too large.

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Georg Gottlob, Marko Samer. 2007-01-14. A Backtracking-Based Algorithm for Computing Hypertree-Decompositions. https://doi.org/10.1145/1412228.1412229

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