The communication complexity of addition

The communication complexity of addition (2011)

by Emanuele Viola

Datum	Value	Source
TITLE	The communication complexity of addition	SVM HeaderParse 0.2
AUTHOR NAME	Emanuele Viola	SVM HeaderParse 0.2
ABSTRACT	Suppose each of k ≤ no(1) players holds an n-bit number xi in its hand. The players wish to determine if ∑ i≤k xi = s. We give a public-coin protocol with error 1% and communication O(k lg k). The communication bound is independent of n, and for k ≥ 3 improves on the O(k lg n) bound by Nisan (Bolyai Soc. Math. Studies; 1993). Our protocol also applies to addition modulo m. In this case we give a matching (public-coin) Ω(k lg k) lower bound for various m. We also obtain some lower bounds over the integers, including Ω(k lg lg k) for protocols that are one-way, like ours. We give a protocol to determine if ∑ xi> s with error 1 % and communication O(k lg k) lg n. For k ≥ 3 this improves on Nisan’s O(k lg 2 n) bound. A similar improvement holds for computing degree-(k − 1) polynomial-threshold functions in the number-on-forehead model. We give a (public-coin, 2-player, tight) Ω(lg n) lower bound to determine if x1> x2. This improves on the Ω ( √ lg n) bound by Smirnov (1988).	SVM HeaderParse 0.2
YEAR	2011	SVM HeaderParse 0.2
CITATIONS	38 found	ParsCit 1.0