Hadamard Tensors and Lower Bounds on Multiparty Communication Complexity

Authors Jeff Ford, Anna Gál

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Jeff Ford
Anna Gál

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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)


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.
  • Multiparty communication complexity
  • lower bounds


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