The communication complexity of the universal relation

G. Tardos, U. Zwick

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Citations (Scopus)

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
Publication statusPublished - Jan 1 1997
Event12th Annual IEEE Conference on Computational Complexity, CCC 1997 - Ulm, Germany
Duration: Jun 24 1997Jun 27 1997

Other

Other12th Annual IEEE Conference on Computational Complexity, CCC 1997
CountryGermany
CityUlm
Period6/24/976/27/97

Fingerprint

Communication Complexity
Communication
Networks (circuits)
Optimality
Correspondence
Lower bound
Upper bound

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Computational Mathematics

Cite this

Tardos, G., & Zwick, U. (1997). The communication complexity of the universal relation. In Proceedings - 12th Annual IEEE Conference on Computational Complexity, CCC 1997 (Formerly: Structure in Complexity Theory Conference) (pp. 247-259). [612320] IEEE Computer Society. https://doi.org/10.1109/CCC.1997.612320

The communication complexity of the universal relation. / Tardos, G.; Zwick, U.

Proceedings - 12th Annual IEEE Conference on Computational Complexity, CCC 1997 (Formerly: Structure in Complexity Theory Conference). IEEE Computer Society, 1997. p. 247-259 612320.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Tardos, G & Zwick, U 1997, The communication complexity of the universal relation. in Proceedings - 12th Annual IEEE Conference on Computational Complexity, CCC 1997 (Formerly: Structure in Complexity Theory Conference)., 612320, IEEE Computer Society, pp. 247-259, 12th Annual IEEE Conference on Computational Complexity, CCC 1997, Ulm, Germany, 6/24/97. https://doi.org/10.1109/CCC.1997.612320
Tardos G, Zwick U. The communication complexity of the universal relation. In Proceedings - 12th Annual IEEE Conference on Computational Complexity, CCC 1997 (Formerly: Structure in Complexity Theory Conference). IEEE Computer Society. 1997. p. 247-259. 612320 https://doi.org/10.1109/CCC.1997.612320
Tardos, G. ; Zwick, U. / The communication complexity of the universal relation. Proceedings - 12th Annual IEEE Conference on Computational Complexity, CCC 1997 (Formerly: Structure in Complexity Theory Conference). IEEE Computer Society, 1997. pp. 247-259
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