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Asymptotically Optimal Lower Bounds on the NIH-Multi-Party Information Complexity of the AND-Function and Disjointness

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Abstract

Here we prove an asymptotically optimal lower bound on the information complexity of the $k$-party disjointness function with the unique intersection promise, an important special case of the well known disjointness problem, and the AND$_k$-function in the number in the hand model. Our $\Omega(n/k)$ bound for disjointness improves on an earlier $\Omega(n/(k \log k))$ bound by Chakrabarti {\it et al.}~(2003), who obtained an asymptotically tight lower bound for one-way protocols, but failed to do so for the general case. Our result eliminates both the gap between the upper and the lower bound for unrestricted protocols and the gap between the lower bounds for one-way protocols and unrestricted protocols.

BibTeX - Entry

@InProceedings{gronemeier:LIPIcs:2009:1846,
  author =	{Andre Gronemeier},
  title =	{{Asymptotically Optimal Lower Bounds on the NIH-Multi-Party Information Complexity of the AND-Function and Disjointness}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{505--516},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Susanne Albers and Jean-Yves Marion},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/1846},
  URN =		{urn:nbn:de:0030-drops-18465},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2009.1846},
  annote =	{Keywords: Computational complexity, Communication complexity}
}

Keywords: Computational complexity, Communication complexity
Seminar: 26th International Symposium on Theoretical Aspects of Computer Science
Issue date: 2009
Date of publication: 2009


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