一种基于回溯的超树分解算法
A Backtracking-Based Algorithm for Computing Hypertree-Decompositions
摘要：
超图的超树分解是图的树分解的推广。对应的超树宽度是对编码计算问题的循环性和因此的易处理性的度量。许多NP-难的决策和计算问题在其结构对应于有界超树宽度的超图的情况下是容易处理的。直觉上，超树宽度越小，计算问题就可以越快地解决。本文提出了一种新的基于回溯的小宽度超树分解算法det-k-decomp。我们的基准评估表明，det-k-decomp显着优于opt-k-decomp，迄今为止唯一的精确超树分解算法。即使与最好的启发式算法相比，只要超图不是太大，我们也得到了有竞争力的结果。
英文摘要：
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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