The communication complexity of the universal relation

G. Tardos, U. Zwick

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Consider the following communication problem. Alice gets a word x∈{0,1}n and Bob gets a word y∈{0,1}n. Alice and Bob are told that xne/y. Their goal is to find an index 1les/iles/n such that xine/yi (the index i should be known to both of them). This problem is one of the most basic communication problems. It arises naturally from the correspondence between circuit depth and communication complexity discovered by M. Karchmer and A. Wigderson (1990). We present three protocols using which Alice and Bob can solve the problem by exchanging at most it n+2 bits. One of this protocols is due to S. Rudich and G. Tardos. These protocols improve the previous upper bound of n+log∗ n, obtained by M. Karchmer. We also show that any protocol for solving the problem must exchange, in the worst case, at least n+1 bits. This improves a simple lower bound of n-1 obtained by Karchmer. Our protocols, therefore, are at most one bit away from optimality.

Original languageEnglish
Title of host publicationProceedings - 12th Annual IEEE Conference on Computational Complexity, CCC 1997 (Formerly
Subtitle of host publicationStructure in Complexity Theory Conference)
PublisherIEEE Computer Society
Pages247-259
Number of pages13
ISBN (Electronic)0818679077
DOIs
StatePublished - 1997
Event12th Annual IEEE Conference on Computational Complexity, CCC 1997 - Ulm, Germany
Duration: 24 Jun 199727 Jun 1997

Publication series

NameProceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)1093-0159

Conference

Conference12th Annual IEEE Conference on Computational Complexity, CCC 1997
Country/TerritoryGermany
CityUlm
Period24/06/9727/06/97

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