Ben Mabrouk B.,Ecole Superieure des science et des Techniques de Tunis |
Hasni H.,Manouba University |
Mahjoub Z.,University of Tunis
2010 ACS/IEEE International Conference on Computer Systems and Applications, AICCSA 2010 | Year: 2010
We address in this paper the design and analysis of cost-optimal parallel algorithms for solving the problem of the longest common subsequence. Starting from the standard sequential dynamic programming algorithm which has the structure of a perfect nest of two embedded loops, we make use of a specific three-step parallelization approach consisting in (i) a dependence analysis within the nest ; (ii) the determination of a particular unimodular transformation leading to a new nest whose second loop is parallel ; (iii) the design of two linear time schedulings for the derived parallel algorithm when a given number of processors is available. The first scheduling is fitted to the nest structure while the second is greedy oriented and optimal. The makespans of the two schedulings are explicitly determined. This permits to establish a comparison showing their respective efficiencies.