UNSPECIFIED (1998) An Omega(root log log n) lower bound for routing in optical networks. In: 1994 ACM Symposium on Parallel Algorithms and Architectures, JUN 27-29, 1994, CAPE MAY, NEW JERSEY.

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Abstract

Optical communication is likely to significantly speed up parallel computation because the vast bandwidth of the optical medium can be divided to produce communication networks of very high degree. However, the problem of contention in high-degree networks makes the routing problem in these networks theoretically (and practically) difficult. In this paper we examine Valiant's h-relation routing problem, which is a fundamental problem in the theory of parallel computing. The h-relation routing problem arises both in the direct implementation of specific parallel algorithms on distributed-memory machines and in the general simulation of shared-memory models such as the PRAM on distributed-memory machines. In an h-relation routing problem each processor has up to h messages that it wishes to send to other processors and each processor is the destination of at most h messages. We present a lower bound for routing an h-relation (for any h > 1) on a complete optical network of size n. Our lower bound applies to any randomized distributed algorithm for this task. Specifically, we show that the expected number of communication steps required to route an arbitrary h-relation is Omega(h+ root log log n). This is the first known lower bound for this problem which does not restrict the class of algorithms under consideration.

Item Type:	Conference Item (UNSPECIFIED)
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software Q Science > QA Mathematics
Journal or Publication Title:	SIAM JOURNAL ON COMPUTING
Publisher:	SIAM PUBLICATIONS
ISSN:	0097-5397
Date:	August 1998
Volume:	27
Number:	4
Number of Pages:	16
Page Range:	pp. 1083-1098
Publication Status:	Published
Title of Event:	1994 ACM Symposium on Parallel Algorithms and Architectures
Location of Event:	CAPE MAY, NEW JERSEY
Date(s) of Event:	JUN 27-29, 1994
URI:	http://wrap.warwick.ac.uk/id/eprint/15738

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