Optimal separations between concurrent-write parallel machines
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Better bounds for threshold formulas
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Lower Bounds on Formula Size of Boolean Functions Using Hypergraph Entropy
SIAM Journal on Discrete Mathematics
Theoretical Computer Science - Special issue on complexity theory and the theory of algorithms as developed in the CIS
Communication complexity
Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
Space lower bounds for distance approximation in the data stream model
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Two applications of information complexity
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Information Theory Methods in Communication Complexity
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Informational Complexity and the Direct Sum Problem for Simultaneous Message Complexity
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
A note on the /spl theta/ number of Lovasz and the generalized Delsarte bound
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
A direct sum theorem in communication complexity via message compression
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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We present a new method for obtaining lower bounds on communication complexity. Our method is based on associating with a binary function f a graph Gf such that log χ(Gf) captures N0(f) + N1(f). Here χ(G) denotes the chromatic number of G, and N0(f) and N1(f) denote, respectively, the nondeterministic communication complexity of f and f. Thus logχ(Gf) is a lower bound on the deterministic as well as zero-error randomized communication complexity of f. Our characterization opens the possibility of using various relaxations of the chromatic number as lower bound techniques for communication complexity. In particular, we show how various (known) lower bounds can be derived by employing the clique number, the Lovász ϑ-function, and graph entropy lower bounds on the chromatic number.