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Photograph used for a newspaper owned by the Oklahoma Publishing Company. Caption: "Wally Heinzel"

Photograph used for a story in the Daily Oklahoman newspaper. Caption: "Wally Heinzel, 77, is one person who makes a difference in the look of central Oklahoma."

Photograph used for a story in the Daily Oklahoman newspaper. Caption: "OSU's Daryl Johnson fights for extra yardage Saturday afternoon against Colorado."

Photograph used for a story in the Daily Oklahoman newspaper. Caption: "Langston University Head Football Coach Greg Johnson."

Photograph used for a story in the Daily Oklahoman newspaper. Caption: "Lions' quarterback Ed Daniels is tripped up by East Central's Carlos Lynn during Saturday's contest in Langston."

Photograph used for a newspaper owned by the Oklahoma Publishing Company. Caption: "State Transportation Department workers repair an expansion link in the Interstate 44 bridge at Airport Road in Oklahoma City on Saturday."

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 …

Photograph used for a newspaper owned by the Oklahoma Publishing Company.

Photograph used for a newspaper owned by the Oklahoma Publishing Company.

Photograph used for a story in the Daily Oklahoman newspaper. Caption: "Oklahoma City's Jeff Massey (26) battles behind the goal with a Fort Worth player during a game this season."

Photograph used for a story in the Daily Oklahoman newspaper. Caption: "Colorado's Dennie Collier (22) sacks (Oklahoma State quarterback) Andy Loveland in Saturday's 31-14 CU win in Stillwater."

Photograph used for a story in the Daily Oklahoman newspaper.

Photograph used for a newspaper owned by the Oklahoma Publishing Company.

Photograph used for a newspaper owned by the Oklahoma Publishing Company.

Photograph used for a story in the Daily Oklahoman newspaper. Caption: "Oklahoma City's Trent Pankewicz tries to find the puck after a save by Fort Worth goalie."

Photograph used for a story in the Daily Oklahoman newspaper. Caption: "The art of fire making."

Photograph used for a story in the Daily Oklahoman newspaper. Caption: "Below, landscape architect Bill renner, visits with Terrie Hubbard, the chairwoman assigned to Renner's house."

Photograph used for a newspaper owned by the Oklahoma Publishing Company.

Photograph used for a newspaper owned by the Oklahoma Publishing Company.

Photograph used for a story in the Daily Oklahoman newspaper. Caption: "OSU's Keith Burns sacks Colorado's Kordell Stewart earlier this season, Burns is one of 21 Cowboy seniors playing their final college game."

Photograph used for a story in the Daily Oklahoman newspaper. Caption: "Eddie Williams of Oklahoma City builds a grass hut while Donna Edmond Williams takes pictures of family members working on the village."

Photograph used for a story in the Daily Oklahoman newspaper. Caption: "OSU linebacker Richie Ansley hounds Colorado QB Kordell Stewart during Saturday's Big Eight contest in Stillwater."

Photograph used for a story in the Daily Oklahoman newspaper. Caption: "Author Bill Sloan autographs copies of his book on Kennedy assassination figures for customers Kris Veitch and his wife Jamie at Bollinger's Books in Oklahoma City."