Inner Product and Set Disjointness: Beyond Logarithmically Many Parties
Article No.: 26, Pages 1 - 28
Abstract
A major goal in complexity theory is to understand the communication complexity of number-on-the-forehead problems f:({0, 1} n)k → {0, 1} with k > log n parties. We study the problems of inner product and set disjointness and determine their randomized communication complexity for every k ≥ log n, showing in both cases that Θ(1 + ⌈log n⌉/ log ⌈1 + k/ log n⌉) bits are necessary and sufficient. In particular, these problems admit constant-cost protocols if and only if the number of parties is k ≥ nϵ for some constant ϵ > 0.
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Index Terms
- Inner Product and Set Disjointness: Beyond Logarithmically Many Parties
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December 2020
156 pages
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Publication History
Published: 25 November 2020
Accepted: 01 August 2020
Received: 01 January 2018
Published in TOCT Volume 12, Issue 4
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- HSE University Basic Research Program
- NSF CAREER award
- Alfred P. Sloan Foundation
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