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...

• Type: Conference
• Year: 2004
• Where: LATIN
• Authors: Endre Boros, Khaled M. Elbassioni, Vladimir Gurvich, Leonid Khachiyan
• Keywords: Information Retrieval, LATIN 2004, Maximal Independent Set, R)-bounded Intersections, finite Set