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Simplified Lower Bounds on the Multiparty Communication Complexity of Disjointness

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Abstract

We show that the deterministic number-on-forehead communication complexity of set disjointness for k parties on a universe of size n is Omega(n/4^k). This gives the first lower bound that is linear in n, nearly matching Grolmusz's upper bound of O(log^2(n) + k^2n/2^k). We also simplify the proof of Sherstov's Omega(sqrt(n)/(k2^k)) lower bound for the randomized communication complexity of set disjointness.

BibTeX - Entry

@InProceedings{rao_et_al:LIPIcs:2015:5076,
  author =	{Anup Rao and Amir Yehudayoff},
  title =	{{Simplified Lower Bounds on the Multiparty Communication Complexity of Disjointness}},
  booktitle =	{30th Conference on Computational Complexity (CCC 2015)},
  pages =	{88--101},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-81-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{33},
  editor =	{David Zuckerman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5076},
  URN =		{urn:nbn:de:0030-drops-50769},
  doi =		{10.4230/LIPIcs.CCC.2015.88},
  annote =	{Keywords: communication complexity, set disjointness, number on forehead, lower bounds}
}

Keywords: communication complexity, set disjointness, number on forehead, lower bounds
Seminar: 30th Conference on Computational Complexity (CCC 2015)
Issue date: 2015
Date of publication: 2015


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