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Complexity of Recognizing Equal Unions in Families of Sets

✍ Scribed by David P. Jacobs; Robert E. Jamison

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 87 KB
Volume: 37
Category: Article
ISSN: 0196-6774
DOI: 10.1006/jagm.2000.1121

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✦ Synopsis

A family of sets has the equal union property if there exist two nonempty disjoint subfamilies having equal unions and has the full equal union property if, in addition, all sets are included. Both recognition problems are NP-complete even when restricted to families for which the cardinality of every set is at most three. Both problems can be solved in polynomial time when restricted to families having a bounded number of sets with cardinality greater than two. A corollary is that deciding if a graph has two disjoint edge covers is in P.

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