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Exact exponential-time algorithms for finding bicliques

By et al. Daniel Binkele-Raible

Abstract

Due to a large number of applications, bicliques of graphs have been widely considered in the literature. This paper focuses on non-induced bicliques. Given a graph G = (V, E) on n vertices, a pair (X, Y), with X, Y ⊆ V, X ∩ Y = ∅, is a non-induced biclique if {x, y} ∈ E for any x ∈ X and y ∈ Y. The NP-complete problem of finding a non-induced (k1, k2)-biclique asks to decide whether G contains a non-induced biclique (X, Y) such that |X | = k1 and |Y | = k2. In this paper, we design a polynomial-space O(1.6914 n)-time algorithm for this problem. It is based on an algorithm for bipartite graphs that runs in time O(1.30052 n). In deriving this algorithm, we also exhibit a relation to the spare allocation problem known from memory chip fabrication

Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.172.6751
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