Fractional Edge Cover Number of Model RB

Model RB is a random constraint satisfaction problem with a growing domain size, which exhibits exact phase transition phenomena. Many hard instances with planted solutions can be generated via Model RB, to be used as benchmarks for algorithmic competitions and researches. In the past, some structural parameters of constraint hypergraphs are analyzed to show hardness of Model RB, such as hinge width, decycling number, treewidth, and hypertree width. In this paper, one more structural parameter of constraint hypergraphs of Model RB, namely the fractional edge cover number, is analyzed. We show upper and lower bounds on the fractional edge cover number of Model RB. In particular, the fractional edge cover number of Model RB is shown to be asymptotically linear in the number of variables, like hinge width, decycling number, treewidth and hypertree width. These results together provide further evidences on the hardness of Model RB.

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