A comparison of two lower-bound methods for communication complexity
MFCS '94 Selected papers from the 19th international symposium on Mathematical foundations of computer science
Communication complexity
On the complexity of communication complexity
Proceedings of the forty-first annual ACM symposium on Theory of computing
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An ordered biclique partition of the complete graph K"n on n vertices is a collection of bicliques (i.e., complete bipartite graphs) such that (i) every edge of K"n is covered by at least one and at most two bicliques in the collection, and (ii) if an edge e is covered by two bicliques then each endpoint of e is in the first class in one of these bicliques and in the second class in the other one. We show in this note that the minimum size of such a collection is O(n^2^/^3). This gives new results on two problems related to communication complexity. Namely, (i) a new separation between the size of a fooling set and the rank of a 0/1-matrix, and (ii) an improved lower bound on the nondeterministic communication complexity of the clique vs. independent set problem are given.