CONTENTS

A PARALLELIZATION SCHEME OF SOME ALGORITHMS 247
3: If the validity conditions are satisfied then i is appended to the sequence of
results.
4: Builds a message with the results and sends it to the dispatcher.
5: end for
Receiving a responce message, the dispatcher verifies whether some solutions are
obtained (i.e. the length of a generated sequence is n). If the generated sequences are
not solutions then the dispatcher push them into the repository.
As initialization, the dispatcher sends a message with the sequence [0] to the first
worker, while the sequences [i], i ∈ {1, . . . , n − 1} are push into the repository.
The quicksort method. The message class contains the rank of the source, a
tag, an index, a splitting index and a sequence.
Let us suppose that at a stage of the quicksort method, the sequence to be sorted
is [x0, x1, . . . , xn−1]. The index of a subsequence [xp, xp+1, . . . , xq] is p. Let us suppose
that the dispatcher sends this subsequence to a worker. The worker split the received
sequence as it is done in the standard quicksort method. If [y0, y1, . . . , yq−p] is the
modified sequence and r is the splitting index, then
yi < yr, ∀i < r and yj ≥ yr ∀j ≥ r.
This sequence will be returned by the worker.
Receiving a response message, the dispatcher update the sequence to be sorted
and if the length of a splited subsequence is greather than 2, then the parameters of
subsequence (the starting index and the length) are pushed into the repository.
References
[1] Z. BAOYIN, 2005, ”Jcluster A Java Parallel Environment.” Docs distributed with the software,
version 1.0.5.
[2] R. BISSELING, 2004, Parallel Scientific Computation. A structured approach using BSP and
MPI, Oxford Univ. Press.
[3] CHENGYAN ZH., 1996, Parallel Quicksort algorithm with PVM optimization. Project report
CS62025. Univ. NewBrunswick, Fac. Computer Science, Fredericton.
[4] HAMADI Y., BESSIÈRE CH., QUINQUETON J., 1998, Backtracking in Distributed Networks.
http://research.microsoft.com/∼youssefh/Papers/ecai98.pdf.
[5] TSIGAS PH., ZHANG Y., 2003, A Simple Fast Parallel Implementation
of Quicksort and its Performance Evaluation on SUN Enterprise 10000.
http://www.es.chalmers.se/∼tsigas/papers/Pquick.pdf.
[6] SNIR M., OTTO D., HUSS-LEDERMAN S., WALKER D., DONGARRA J., 1996, MPI: The
Complete Reference. MIT Press, Cambridge, MA.
[7] SCHEIBER E., 2007, A TSpaces Based Framework for Parallel - Distributed Applications.
Knowledge Engineering Principles and Techniques 1 (2007), Cluj University Press, 341-345.