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Communication complexity of algebraic computation

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2 Author(s)
Z. -Q. Luo ; Dept. of Electr. & Comput. Eng., McMaster Univ., Hamilton, Ont., Canada ; J. N. Tsitsiklis

The authors consider a situation in which two processors P1 and P2 are to evaluate one or more functions f1, . . ., fs of two vector variables x and y, under the assumption that processor P1 (respectively, P2 ) has access only to the value of x (respectively, y ) and the functional form of f1, . . ., f s. They consider a continuous model of communication whereby real-valued messages are transmitted, and they study the minimum number of messages required for the desired computation. Tight lower bounds are established for the following three problems: (1) each f i is a rational function and only one-way communication is allowed. (2) The variables x and y are matrices and the processors wish to solve the linear system (x+y) z=b for the unknown z. (3) The processors wish to evaluate a particular root of the polynomial equation Σ( xi+yi)zi=0, where the sum is from i=0 to n-1

Published in:

Foundations of Computer Science, 1990. Proceedings., 31st Annual Symposium on

Date of Conference:

22-24 Oct 1990