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Large hypertree width for sparse random hypergraphs

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Abstract

Hypertree width is a graph-theoretic parameter similar to treewidth. It has many equivalent characterizations and many applications. If the hypertree width of the constraint graphs of the instances of a constraint satisfaction problem is bounded by a constant, then the CSP is tractable In this paper, we show that with high probability, hypertree width is large on sparse random \(k\)-uniform hypergraphs. Our results provide further theoretical evidence on the hardness of some random constraint satisfaction problems, called Model RB and Model RD, around the satisfiability phase transition points.

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Acknowledgments

We thank Professor Kaile Su for his encouragement and support. We also thank the unknown referees for helpful comments. Partially supported by National 973 Program of China (Grant No. 2010CB328103) and Natural Science Foundation of China (Grant Nos. 61370156 and 61370052).

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Authors and Affiliations

  1. Key Laboratory of High Confidence Software Technologies, Ministry of Education, School of Electronic Engineering and Computer Science, Institute of Software, Peking University, Beijing, 100871, China

    Tian Liu & Chaoyi Wang

  2. National Lab of Software Development Environment, Beihang University, Beijing, 100191, China

    Ke Xu

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  1. Tian Liu
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  2. Chaoyi Wang
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  3. Ke Xu
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Correspondence to Tian Liu or Ke Xu.

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Liu, T., Wang, C. & Xu, K. Large hypertree width for sparse random hypergraphs. J Comb Optim 29, 531–540 (2015). https://doi.org/10.1007/s10878-013-9704-y

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