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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.06111.9
URN: urn:nbn:de:0030-drops-6076
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2006/607/
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Ford, Jeff ;
Gál, Anna
Hadamard Tensors and Lower Bounds on Multiparty Communication Complexity
Abstract
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
@InProceedings{ford_et_al:DagSemProc.06111.9,
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 = {https://drops.dagstuhl.de/opus/volltexte/2006/607},
URN = {urn:nbn:de:0030-drops-6076},
doi = {10.4230/DagSemProc.06111.9},
annote = {Keywords: Multiparty communication complexity, lower bounds}
}
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Keywords: |
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Multiparty communication complexity, lower bounds |
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Collection: |
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06111 - Complexity of Boolean Functions |
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Issue Date: |
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2006 |
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Date of publication: |
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09.10.2006 |
