Tradeoffs between communication and space

Authors:
T. Lam;P. Tiwari;M. Tompa
Affiliations:
Department of Computer Science, University of Hong Kong, Pokfulam Road, Hong Kong;IBM Research Division, Thomas J. Watson Research Center, P. O. Box 218, Yorktown Heights, New York;IBM Research Division, Thomas J. Watson Research Center, P. O. Box 218, Yorktown Heights, New York
Venue:
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Year:
1989

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Abstract

This paper initiates the study of communication complexity when the processors have limited work space. The following tradeoffs between number C of communications steps and space S are proved:For multiplying two n × n matrices in the arithmetic model with two-way communication, CS = &THgr;(n2).For convolution of two degree n polynomials in the arithmetic model with two-way communication, CS = &THgr;(n2).For multiplying an n × n matrix by an n-vector in the Boolean model with one-way communication, CS = &THgr;(n2).In contrast, the discrete Fourier transform and sorting can be accomplished in &Ogr;(n) communication steps and &Ogr;(log n) space simultaneously, and the search problems of Karchmer and Wigderson associated with any language in NCk can be solved in &Ogr;(logk n) communication steps and &Ogr;(logk n) space simultaneously.