Hadamard Tensors and Lower Bounds on Multiparty Communication Complexity

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 Ω(n/2k) multiparty communication complexity. We also exhibit constructions of Hadamard tensors, giving Ω(n/2k) lower bounds on multiparty communication complexity for a new class of explicitly defined Boolean functions.

• Type: Conference
• Year: 2005
• Where: ICALP
• Authors: Jeff Ford, Anna Gál
• Keywords: ICALP 2005, Multiparty Communication, Multiparty Communication Complexity, Multiparty Communication Problems, Theoretical Computer Science