On finding acyclic subhypergraphs

Authors:
Kouichi Hirata;Megumi Kuwabara;Masateru Harao
Affiliations:
Department of Artificial Intelligence;Kyushu Institute of Technology, Graduate School of Computer Science and Systems Engineering, Iizuka, Japan;Department of Artificial Intelligence
Venue:
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Year:
2005

Citing 14
Cited 2

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Abstract

In this paper, we investigate the problem of finding acyclic subhypergraphs in a hypergraph. First we show that the problem of determining whether or not a hypergraph has a spanning connected acyclic subhypergraph is NP-complete. Also we show that, for a given K 0, the problem of determining whether or not a hypergraph has an acyclic subhypergraph containing at least Khyperedges is NP-complete. Next, we introduce a maximal acyclic subhypergraph, which is an acyclic subhypergraph that is cyclic if we add any hyperedge of the original hypergraph to it. Then, we design the linear-time algorithm mas to find it, which is based on the acyclicity test algorithm designed by Tarjan and Yannakakis (1984).