Max-Plus Algebra and Discrete Event Simulation on Parallel Hierarchical Heterogeneous Platforms

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6586)


In this paper we explore computing max-plus algebra operations and discrete event simulations on parallel hierarchal heterogeneous platforms. When performing such tasks on heterogeneous platforms parameters such as the total volume of communication and the top-level data partitioning strategy must be carefully taken into account. Choice of the partitioning strategy is shown to greatly affect the overall performance of these applications due to different volumes of inter-partition communication that various strategies impart on these operations. One partitioning strategy in particular is shown to reduce the execution times of these operations more than other, more traditional strategies. The main goal of this paper is to present benefits waiting to be exploited by the use of max-plus algebra operations on these platforms and thus speeding up more complex and quite common computational topic areas such as discrete event simulation.


Data Partitioning Heterogeneous Computing Parallel Computing Tropical Algebra Max-Plus algebra Discrete Event Simulation Hierarchal Algorithms Square-Corner Partitioning 


  1. 1.
    Beaumont, O., et al.: Partitioning a Square into Rectangles: NP-Completeness and Approximation Algorithms. Algorithmica 34(3), 217–239 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Becker, B., Lastovetsky, A.: Data partitioning for matrix multiplication on two interconnected processors. In: Cluster 2006. IEEE, Los Alamitos (2006)Google Scholar
  3. 3.
    Becker, B.A., Lastovetsky, A.: Towards data partitioning for parallel computing on three interconnected clusters. In: ISPDC 2007 (2007)Google Scholar
  4. 4.
    Comet, J.: Application of max-plus algebra to biological sequence comparisons. Theoretical Computer Science 293, 189–217 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    De Schutter, B., De Moor, B.: On the sequence of consecutive matrix powers of boolean matrices in the max-plus algebra. In: Tornamb, A., Conte, G., Perdon, A.M. (eds.) Theory and Practice of Control and Systems, pp. 672–677 (1999)Google Scholar
  6. 6.
    Fersha, A.: Parallel and distributed simulation of discrete event systems. In: Handbook of Parallel and Distributed Computing. McGraw-Hill, New York (1995)Google Scholar
  7. 7.
    Fishman, G.S.: Discrete-Event Simulation: Modeling, Programming, and Analysis. Springer, New York (2001)CrossRefzbMATHGoogle Scholar
  8. 8.
    Gaubert, S., Plus, M.: Methods and applications of (max,+) linear algebra. In: STACS 2007. LNCS, vol. 3088. Springer, Heidelberg (2007)Google Scholar
  9. 9.
    Heidergott, B., Jan Olsder, G., van der Woude, J.: Max Plus at Work. Princeton University Press, Princeton (2006)zbMATHGoogle Scholar
  10. 10.
    Kalinov, A., Lastovetsky, A.: Heterogeneous Distribution of Computations While Solving linear algebra Problems on Networks of Heterogeneous Computers. In: Sloot, P.M.A., Hoekstra, A.G., Bubak, M., Hertzberger, B. (eds.) HPCN-Europe 1999. LNCS, vol. 1593. Springer, Heidelberg (1999)Google Scholar
  11. 11.
    Kirov, M.V.: The transfer-matrix and max-plus algebra method for global combinatorial optimization: Application to cyclic and polyhedral water clusters. Physica A 388, 1432–1445 (2009)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Lastovetsky, L., Dongarra, J.: High Performance Heterogeneous Computing. Wiley-Blackwell, Hoboken (2009)CrossRefGoogle Scholar
  13. 13.
    Tacconi, D., Lewis, F.: A new matrix model for discrete event systems. application to simulation. IEEE Control Systems 97, 6–71 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of Computer Science and InformaticsUniversity College DublinDublinIreland

Personalised recommendations