Polynomial recognition of equal unions in hypergraphs with few vertices of large degree

Authors:
David P. Jacobs;Robert E. Jamison
Affiliations:
Clemson University, Department of Computer Science, Clemson, SC 29634 USA;Clemson University, Department of Mathematical Sciences, Clemson, SC 29634 USA
Venue:
Journal of Discrete Algorithms
Year:
2006

Citing 4
Cited 0

Complexity of recognizing equal unions in families of sets

Journal of Algorithms
A note on equal unions in families of sets

Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
On the complexity of sign-nonsingularity and equal unions of sets

ACM-SE 38 Proceedings of the 38th annual on Southeast regional conference

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Abstract

A family of nonempty sets has the equal union property if there exist two nonempty disjoint subfamilies having equal unions. If every point belongs to the unions, then we say the family has the full equal union property. Recognition of both properties is NP-complete even when restricted to families for which the degree of every point is at most three. In this paper we show that both recognition problems can be solved in polynomial time for families in which there is a bound on the number of points whose degree exceeds two.