A Backtracking-Based Algorithm for Computing Hypertree-Decompositions

TL;DR

This paper introduces a new backtracking algorithm for computing hypertree decompositions, which are crucial for solving complex problems efficiently on hypergraphs with bounded hypertree-width.

Contribution

The paper presents det-k-decomp, a novel backtracking-based algorithm that outperforms existing exact methods in computing hypertree decompositions.

Findings

det-k-decomp significantly outperforms opt-k-decomp in benchmarks.

The algorithm achieves competitive results with heuristics on smaller hypergraphs.

Hypertree decompositions facilitate tractable solutions for NP-hard problems.

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.