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Conference Papers Year : 2014

Biclique Coverings, Rectifier Networks and the Cost of ε-Removal

Abstract

We relate two complexity notions of bipartite graphs: the minimal weight biclique covering number Cov(G) and the minimal rec-tifier network size Rect(G) of a bipartite graph G. We show that there exist graphs with Cov(G) ≥ Rect(G) 3/2−ǫ . As a corollary, we estab-lish that there exist nondeterministic finite automata (NFAs) with ε-transitions, having n transitions total such that the smallest equivalent ε-free NFA has Ω(n 3/2−ǫ) transitions. We also formulate a version of previous bounds for the weighted set cover problem and discuss its con-nections to giving upper bounds for the possible blow-up.
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Dates and versions

hal-01079368 , version 1 (01-11-2014)

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Szabolcs Iván, Ádám Lelkes, Judit Nagy-György, Balázs Szörényi, György Turán. Biclique Coverings, Rectifier Networks and the Cost of ε-Removal. 16th International Workshop on Descriptional Complexity of Formal Systems, Proceedings, Aug 2014, Turku, Finland. pp.174 - 185, ⟨10.1007/978-3-319-09704-6_16⟩. ⟨hal-01079368⟩
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