Clique problem, cutting plane proofs and communication complexity

Authors:
Stasys Jukna
Affiliations:
Institute of Computer Science, University of Frankfurt, Frankfurt a.M., Germany and Institute of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania
Venue:
Information Processing Letters
Year:
2012

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Abstract

Motivated by its relation to the length of cutting plane proofs for the Maximum Biclique problem, we consider the following communication game on a given graph G with maximum bipartite clique size K. Two parties separately receive disjoint subsets A, B of vertices such that |A|+|B|K. The goal is to identify a nonedge between A and B. We prove that O(logn) bits of communication are enough for any n-vertex graph.