Parallel solutions of simple indexed recurreno equations

Yosi Ben-Asher, Gady Haber

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We consider a type of recurrence equations called "Simple Indexed Recurrences" (SIR) wherein ordinary recurrences of the form X[i] = opi(X[i -1], X[i]) (i = 1. n) are extended to X[g(i)]=opi(X[f(i)], X[g(i)]) such that opi is an associative binary operation, f,g : {l.n}→ {l.m} and g is distinct. This extends our capabilties for parallelizing loops of the form: for i = 1 to n { X[i] = opi(X[i - l],X[i]) } to the form: for i = 1 to n { X[g(i)] = opi(X[f(i)],X[g(i)}) }. An efficient solution is presented for the special case where we know how to compute the inverse of opi operator. The algorithm requires 0(log n) steps with 0(n/logn) processors. Furthermore, we present a practical and a more improved version of the non-optimal algorithm for SIR presented in [1] which uses repeated iterations of pointer jumping. A sequence of experiments was performed to test the effect of synchronous and asynchronous message-passing executions of the algorithm for p << n processors. This algorithm computes the final values of XQ in □ n/p log p steps and n : log p work, with p processors. The experiments show that pointer jumping requires 0(n) work in most practical cases of SIR loops, thus forming a more practical solution.

Original languageEnglish
Title of host publicationEuro-Par 1998 Parallel Processing - 4th International Conference, Proceedings
PublisherSpringer Verlag
Number of pages7
ISBN (Print)3540649522, 9783540649526
StatePublished - 1998
Event4th International Conference on Parallel Processing, Euro-Par 1998 - Southampton, United Kingdom
Duration: 1 Sep 19984 Sep 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1470 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference4th International Conference on Parallel Processing, Euro-Par 1998
Country/TerritoryUnited Kingdom

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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