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LATIN
2004
Springer

Generating Maximal Independent Sets for Hypergraphs with Bounded Edge-Intersections

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Generating Maximal Independent Sets for Hypergraphs with Bounded Edge-Intersections
Given a finite set V , and integers k ≥ 1 and r ≥ 0, denote by A(k, r) the class of hypergraphs A ⊆ 2V with (k, r)-bounded intersections, i.e. in which the intersection of any k distinct hyperedges has size at most r. We consider the problem MIS(A, I): given a hypergraph A and a subfamily I ⊆ I(A), of its maximal independent sets (MIS) I(A), either extend this subfamily by constructing a new MIS I ∈ I(A) \ I or prove that there are no more MIS, that is I = I(A). We show that for hypergraphs A ∈ A(k, r) with k + r ≤ const, problem MIS(A, I) is NC-reducible to problem MIS(A , ∅) of generating a single MIS for a partial subhypergraph A of A. In particular, for this class of hypergraphs, we get an incremental polynomial algorithm for generating all MIS. Furthermore, combining this result with the currently known algorithms for finding a single maximal independent set of a hypergraph, we obtain efficient parallel algorithms for incrementally generating all MIS for hypergra...
Endre Boros, Khaled M. Elbassioni, Vladimir Gurvic
Added 02 Jul 2010
Updated 02 Jul 2010
Type Conference
Year 2004
Where LATIN
Authors Endre Boros, Khaled M. Elbassioni, Vladimir Gurvich, Leonid Khachiyan
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