DagSemProc.06111.9.pdf
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Hadamard Tensors and Lower Bounds on Multiparty Communication Complexity
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Dagstuhl Seminar Proceedings, Volume 6111
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2006-10-09
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Jeff Ford and Anna Gál. Hadamard Tensors and Lower Bounds on Multiparty Communication Complexity. In Complexity of Boolean Functions. Dagstuhl Seminar Proceedings, Volume 6111, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)
https://doi.org/10.4230/DagSemProc.06111.9
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.
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- Multiparty communication complexity
- lower bounds
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