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  • Large Hinge Width on Sparse Random Hypergraphs

    Author(s)
    Liu, Tian
    Lin, Xiaxiang
    Wang, Chaoyi
    Su, Kaile
    Xu, Ke
    Griffith University Author(s)
    Su, Kaile
    Year published
    2011
    Metadata
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    Abstract
    Consider random hypergraphs on n vertices, where each k-element subset of vertices is selected with probability p independently and randomly as a hyperedge. By sparse we mean that the total number of hyperedges is O(n) or O(n ln n). When k = 2, these are exactly the classical Erd诳-R䥮yi random graphs G(n, p). We prove that with high probability, hinge width on these sparse random hypergraphs can grow linearly with the expected number of hyperedges. Some random constraint satisfaction problems such as Model RB and Model RD have satisfiability thresholds on these sparse constraint hypergraphs, thus the large hinge width results ...
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    Consider random hypergraphs on n vertices, where each k-element subset of vertices is selected with probability p independently and randomly as a hyperedge. By sparse we mean that the total number of hyperedges is O(n) or O(n ln n). When k = 2, these are exactly the classical Erd诳-R䥮yi random graphs G(n, p). We prove that with high probability, hinge width on these sparse random hypergraphs can grow linearly with the expected number of hyperedges. Some random constraint satisfaction problems such as Model RB and Model RD have satisfiability thresholds on these sparse constraint hypergraphs, thus the large hinge width results provide some theoretical evidence for random instances around satisfiability thresholds to be hard for a standard hinge-decomposition based algorithm. We also conduct experiments on these and other kinds of random graphs with several hundreds vertices, including regular random graphs and power law random graphs. The experimental results also show that hinge width can grow linearly with the number of edges on these different random
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    Conference Title
    IJCAI 2011
    Publisher URI
    http://ijcai.org/papers11/contents.php
    Subject
    Applied mathematics not elsewhere classified
    Publication URI
    http://hdl.handle.net/10072/48761
    Collection
    • Conference outputs

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