Limits to parallel computation: P-completeness theory
Limits to parallel computation: P-completeness theory
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
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Journal of the ACM (JACM)
Degrees of acyclicity for hypergraphs and relational database schemes
Journal of the ACM (JACM)
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Computers and Intractability; A Guide to the Theory of NP-Completeness
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LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
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FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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Theory of Computing Systems
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We investigate the computational complexity of two decision problems concerning the existence of certain acyclic subhypergraphs of a given hypergraph, namely the SPANNING ACYCLIC SUBHYPERGRAPH problem and the MAXIMUM ACYCLIC SUBHYPERGRAPH problem. The former is about the existence of an acyclic subhypergraph such that each vertex of the input hypergraph is contained in at least one hyperedge of the subhypergraph. The latter is about the existence of an acyclic subhypergraph with k hyperedges where k is part of the input. For each of these problems, we consider different notions of acyclicity of hypergraphs: Berge-acyclicity, γ-acyclicity, β-acyclicity and α-acyclicity. We are also concerned with the size of the hyperedges of the input hypergraph. Depending on these two parameters (notion of acyclicity and size of the hyperedges), we try to determine which instances of the two problems are in P ∩ RNC and which are NP-complete.