Partition arguments in multiparty communication complexity

Jan Draisma, Eyal Kushilevitz, Enav Weinreb

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Consider the "Number in Hand" multiparty communication complexity model, where k players holding inputs x1,⋯,x k∈{0,1}n communicate to compute the value f(x 1,⋯,xk) of a function f known to all of them. The main lower bound technique for the communication complexity of such problems is that of partition arguments: partition the k players into two disjoint sets of players and find a lower bound for the induced two-party communication complexity problem. In this paper, we study the power of partition arguments. Our two main results are very different in nature: (i) For randomized communication complexity, we show that partition arguments may yield bounds that are exponentially far from the true communication complexity. Specifically, we prove that there exists a 3-argument function f whose communication complexity is Ω(n), while partition arguments can only yield an Ω(log n) lower bound. The same holds for nondeterministiccommunication complexity. (ii) For deterministic communication complexity, we prove that finding significant gaps between the true communication complexity and the best lower bound that can be obtained via partition arguments, would imply progress on a generalized version of the "log-rank conjecture" in communication complexity. We also observe that, in the case of computing relations (search problems), very large gaps do exist. We conclude with two results on the multiparty "fooling set technique", another method for obtaining communication complexity lower bounds.

Original languageEnglish
Pages (from-to)2611-2622
Number of pages12
JournalTheoretical Computer Science
Volume412
Issue number24
DOIs
StatePublished - 27 May 2011
Externally publishedYes

Keywords

  • Communication complexity
  • Log rank conjecture
  • Lower bounds
  • Multiparty communication complexity
  • Partition arguments

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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