On randomized one-round communication complexity

Ilan Kremer*, Noam Nisan, Dana Ron

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

130 Scopus citations

Abstract

We present several results regarding randomized one-round communication complexity. Our results include a connection to the VC-dimension, a study of the problem of computing the inner product of two real valued vectors, and a relation between "simultaneous" protocols and one-round protocols.

Original languageAmerican English
Pages (from-to)21-49
Number of pages29
JournalComputational Complexity
Volume8
Issue number1
DOIs
StatePublished - 1999

Bibliographical note

Funding Information:
It follows from this claim, that in at least 1− 1=8 of the sub-rows in A1[A0, the relative weight of entries with value 0 is at least 0(1 − 1=8). Since R is good, in particular, it is good-in-rows. For < 2−8, 1 − 1=8 > 1=4, and thus necessarily 0 < 1=4=(1 − 1=8) which is less than 2 1=4. 2 Acknowledgments. We would like to thank Oded Goldreich, Nati Linial, Amnon Ta-Shama and Avi Wigderson for many helpful discussions. We would also like to thank an anonymous referee for very detailed and helpful comments. Noam Nisan would like to acknowledge the support of a BSF grant 92-00043 and a Wolfeson award administered by the Israeli Academy of Sciences. Dana Ron would like to acknowledge the support of the Eshkol Fellowship administered by the Israeli Ministry of Sciences, and a National Science Foundation Postdoctoral Research Fellowship, Grant No. DMS-9508963.

Keywords

  • Communication complexity
  • One-round and simultaneous protocols
  • VC-dimension

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