Rapid mixing of hypergraph independent sets
نویسندگان
چکیده
منابع مشابه
Rapid Mixing of Hypergraph Independent Set
We prove that the the mixing time of the Glauber dynamics for sampling independent sets on n-vertex k-uniform hypergraphs is Opn log nq when the maximum degree ∆ satisfies ∆ ď c2k{2, improving on the previous bound [BDK06] of ∆ ď k ́ 2. This result brings the algorithmic bound to within a constant factor of the hardness bound of [BGG`16] which showed that it is NP-hard to approximately count in...
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The study of extremal problems related to independent sets in hypergraphs is a problem that has generated much interest. While independent sets in graphs are defined as sets of vertices containing no edges, hypergraphs have different types of independent sets depending on the number of vertices from an independent set allowed in an edge. We say that a subset of vertices is jindependent if its i...
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GIVEN a set X and a natural number r denote by X(r) the set of relement subsets of X. An r-graph or hypergraph G is a pair (V, T), where V is a finite set and T c V(r) . We call v E V a vertex of G and z cT an r-tuple or an edge of G . Thus a 1-graph is a set V and a subset T of V. As the structure of 1-graphs is trivial, throughout the note we suppose r > 2. A 2-graph is a graph in the sense o...
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Approximate counting via correlation decay is the core algorithmic technique used in the sharp delineation of the computational phase transition that arises in the approximation of the partition function of anti-ferromagnetic two-spin models. Previous analyses of correlation-decay algorithms implicitly depended on the occurrence of strong spatial mixing. This, roughly, means that one uses worst...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2018
ISSN: 1042-9832,1098-2418
DOI: 10.1002/rsa.20830