On a Parallel Algorithm for the Determination of Multiple Optimal Solutions for the LCSS Problem

  • Bchira Ben MabroukEmail author
  • Hamadi Hasni
  • Zaher Mahjoub
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10048)


For particular real world combinatorial optimization problems e.g. the longest common subsequence problem (LCSSP) from Bioinformatics, determining multiple optimal solutions (DMOS) is quite useful for experts. However, for large size problems, this may be too time consuming, thus the resort to parallel computing. We address here the parallelization of an algorithm for DMOS for the LCSSP. Considering the dynamic programming algorithm solving it, we derive a generic algorithm for DMOS (A-DMOS). Since the latter is a non perfect DO-loop nest, we adopt a three-step approach. The first consists in transforming the A-DMOS into a perfect nest. The second consists in choosing the granularity and the third carries out a dependency analysis in order to determine the type of each loop i.e. either parallel or serial. The practical performances of our approach are evaluated through experimentations achieved on input benchmarks and random DNA sequences and targeting a parallel multicore machine.


Bioinformatics Combinatorial optimization problem Dependency analysis Dynamic programming Longest common subsequence Loop nest Multiple optimal solutions Multicore machine Parallelization Polyhedral algorithm 


  1. 1.
    Passaro, A., Starita, A.: Particle swarm optimization for multimodal functions: a clustering approach. J. Artif. Evol. Appl. 8, 1–15 (2008)CrossRefGoogle Scholar
  2. 2.
    Mabrouk, B.B., Hasni, H., Mahjoub, Z.: Parallelization of the dynamic programming algorithm for solving the longest common subsequence problem. In: 8th ACS/IEEE International Conference on Computer Systems and Applications (AICCSA 2010), Hammamet, Tunisia, pp. 1–8 (2010)Google Scholar
  3. 3.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction à l’algorithmique. Dunod, Paris (2002)Google Scholar
  4. 4.
    Aho, A.V., Ullman, J.D.: Foundations of Computer Science. Principles of Computer Science Series. W.H. Freeman & Co., C edition, New York (1995)zbMATHGoogle Scholar
  5. 5.
    Greenberg, R.I.: Bounds on the number of longest common subsequences. Technical report, Department of Mathematical and Computer Sciences, Loyola University, Chicago, USA (2003)Google Scholar
  6. 6.
    Greenberg, R.I.: Fast and simple computation of all longest common subsequences. Technical report, Department of Mathematical and Computer Sciences, Loyola University, Chicago, USA (2011)Google Scholar
  7. 7.
    Wang, Y., Li, H., Yen, G.G., Song, W.: MOMMOP: multiobjective optimization for locating multiple optimal solutions of multimodal optimization problems. J. IEEE Trans. Cybern. 45(4), 830–843 (2015)CrossRefGoogle Scholar
  8. 8.
    Mabrouk, B.B., Hasni, H., Mahjoub, Z.: On determining multiple optimal solutions for dynamic programming problems-application to the longest common subsequence problem. In: 31st International Conference on Computers and Their Applications (CATA 21016), Las Vegas, NV, USA (2016)Google Scholar
  9. 9.
    Megson, G.M., Chen, X.: Automatic Parallelization for a Class of Regular Computations. World Scientific Publishing Co., River Edge (1997)CrossRefzbMATHGoogle Scholar
  10. 10.
    Ssas, R., Mutka, M: Enabling unimodular transformations. In: ACM/IEEE Conference on Supercomputing, Washington, USA, pp. 753–762 (1996)Google Scholar
  11. 11.
    Grama, A., Karypis, G., Kumar, V., Gupta, A.: Introduction to Parallel Computing. Addison Wesley, Boston (2003)zbMATHGoogle Scholar
  12. 12.
    Gengler, M., Ubéda, S., Desprez, F.: Initiation au Parallélisme. Masson, Paris (1996)Google Scholar
  13. 13.
    Quin, M.J.: Parallel programming in C with MPI and OpenMP, International edn. McGraw-Hill Higher Education, Pennsylvania (2003)Google Scholar
  14. 14.
    Cosnard, M., Trystram, D.: Algorithmes et Architectures Parallèles. InterEditions, Paris (1993)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Bchira Ben Mabrouk
    • 1
    Email author
  • Hamadi Hasni
    • 2
  • Zaher Mahjoub
    • 1
  1. 1.Faculty of Sciences of TunisUniversity of Tunis El Manar, University CampusTunisTunisia
  2. 2.Higher School of Technology and Computer ScienceTunisTunisia

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