An {Omega}({radical}log log n) lower bound for routing in optical networks

Conference · Sat Nov 06 04:00:00 EST 1993

OSTI ID:10107445

Goldberg, L A ^[1]; Jerrum, M ^[2]; MacKenzie, P D ^[3]

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1. Sandia National Labs., Albuquerque, NM (United States)
2. Edinburgh Univ. (United Kingdom). Dept. of Computer Science
3. Texas Univ., Austin, TX (United States). Dept. of Computer Sciences

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 + {radical}log log n). This is the first known lower bound for this problem which does not restrict the class of algorithms under consideration.

• Research Organization: Sandia National Labs., Albuquerque, NM (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States); Science and Engineering Research Council, Swindon (United Kingdom)
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 10107445
• Report Number(s): SAND--93-2704C; CONF-940563--1; ON: DE94003800; BR: GB0103012; CNN: Grant GR/F 90363; Grant 003658480
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200
ARRAY PROCESSORS
COMPUTER NETWORKS
DISTRIBUTED DATA PROCESSING
FIBER OPTICS
MATHEMATICS AND COMPUTERS
PARALLEL PROCESSING