By Topic

The strict time lower bound and optimal schedules for parallel prefix with resource constraints

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Haigeng Wang ; Tibco Inc., Palo Alto, CA, USA ; Nicolau, A. ; Siu, K.-Y.S.

Prefix computation is a basic operation at the core of many important applications, e.g., some of the Grand Challenge problems, circuit design, digital signal processing, graph optimizations, and computational geometry. In this paper, we present new and strict time-optimal parallel schedules for prefix computation with resource constraints under the concurrent-read-exclusive-write (CREW) parallel random access machine (PRAM) model. For prefix of N elements on p processors (p independent of N) when N>p(p+1)/2, we derive Harmonic Schedules that achieve the strict optimal time (steps), [2(N-1)/(p+1)]. We also derive Pipelined Schedules that have better program-space efficiency than the Harmonic Schedule, yet only require a small constant number of steps more than the optimal time achieved by the Harmonic Schedule, Both the Harmonic Schedules and the Pipelined Schedules are simple and easy to implement. For prefix of N elements on p processors (p independent of N) where N⩽p(p+1)/2, the Harmonic Schedules are not time-optimal. For these cases, we establish an optimization method for determining key parameters of time-optimal schedules, based on connections between the structure of parallel prefix and Pascal's triangle. Using the derived parameters, we devise an algorithm to construct such schedules. For a restricted class of values of N and p, we prove that the constructed schedules are strictly time-optimal. We also give strong empirical evidence that our algorithm constructs strict time optimal schedules for all cases where N⩽p(p+1)/2

Published in:

Computers, IEEE Transactions on  (Volume:45 ,  Issue: 11 )