Chapter

FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science

Volume 4855 of the series Lecture Notes in Computer Science pp 228-240

Communication Lower Bounds Via the Chromatic Number

  • Ravi KumarAffiliated withYahoo! Research
  • , D. SivakumarAffiliated withGoogle, Inc.

* Final gross prices may vary according to local VAT.

Get Access

Abstract

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 G f such that logχ(G f ) captures N 0(f) + N 1(f). Here χ(G) denotes the chromatic number of G, and N 0(f) and N 1(f) denote, respectively, the nondeterministic communication complexity of \(\overline{f}\) and f. Thus logχ(G f ) 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.