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Ford, Jeff ; Gál, Anna

Hadamard Tensors and Lower Bounds on Multiparty Communication Complexity

06111.GalAnna.Paper.607.pdf (0.2 MB)


We develop a new method for estimating the discrepancy of tensors associated with multiparty communication problems in the ``Number on the Forehead'' model of Chandra, Furst and Lipton. We define an analogue of the Hadamard property of matrices for tensors in multiple dimensions and show that any $k$-party communication problem represented by a Hadamard tensor must have $Omega(n/2^k)$ multiparty communication complexity. We also exhibit constructions of Hadamard tensors, giving $Omega(n/2^k)$ lower bounds on multiparty communication complexity for a new class of explicitly defined Boolean functions.

BibTeX - Entry

  author =	{Jeff Ford and Anna G{\'a}l},
  title =	{Hadamard Tensors and Lower Bounds on Multiparty Communication Complexity},
  booktitle =	{Complexity of Boolean Functions},
  year =	{2006},
  editor =	{Matthias Krause and Pavel Pudl{\'a}k and R{\"u}diger Reischuk and Dieter van Melkebeek},
  number =	{06111},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: Multiparty communication complexity, lower bounds}

Keywords: Multiparty communication complexity, lower bounds
Collection: 06111 - Complexity of Boolean Functions
Issue Date: 2006
Date of publication: 09.10.2006

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