When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.06111.9
URN: urn:nbn:de:0030-drops-6076
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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 =	{Ford, Jeff and G\'{a}l, Anna},
  title =	{{Hadamard Tensors and Lower Bounds on Multiparty Communication Complexity}},
  booktitle =	{Complexity of Boolean Functions},
  pages =	{1--20},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6111},
  editor =	{Matthias Krause and Pavel Pudl\'{a}k and R\"{u}diger Reischuk and Dieter van Melkebeek},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-6076},
  doi =		{10.4230/DagSemProc.06111.9},
  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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