Skip to main content
SpringerLink
Log in

Parallel computation of continuous Petri nets based on hypergraph partitioning

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

Abstract

Continuous Petri net can be used for performance analysis or static analysis. The analysis is based on solving the associated ordinary differential equations. This paper presents a method to parallel compute these differential equations. We first map the Petri net to a hypergraph, and then partition the hypergraph to minimize interprocessor communication while maintaining a good load balance; Based on the partition result, we divide the differential equations into several blocks; Finally, we design a parallel computing algorithm to compute these equations. Software hMETIS is used to partition the hypergraph, and software SUNDIALS is used to support the parallel computing of differential equations. Gas station problem and dining philosopher problem have been used to demonstrate the feasibility, accuracy, and scalability of our method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Akl SG (1997) Parallel computation models and methods. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  2. Alimonti P, Feuerstein E (1993) Petri nets, hypergraphs and conflicts. In: Graph-theoretic concepts in computer science, vol 657, pp 293–309

    Chapter  Google Scholar 

  3. Avrunin GS, Buy UA, Corbett JC, Dillon LK, Wileden JC (1991) Automated analysis of concurrent systems with the constrained expression toolset. IEEE Trans Softw Eng 17(11):1204–1222

    Article  Google Scholar 

  4. Böhm C, Jacopini G (1966) Flow diagram, Turing machines and languages with only two formation rules. Commun ACM 9(5):366–371

    Article  MATH  Google Scholar 

  5. Burch JR, Clarke EM, Long DE (1991) Representing circuits more efficiently in symbolic model checking. In: Proceedings of the 28th design automation conference. IEEE Computer Society Press, Los Alamitos, pp 403–407

    Google Scholar 

  6. Burrage K (1995) Parallel and sequential methods for ordinary differential equations. Oxford Science Publications

  7. Çatalyürek Ü, Aykanat C (1999) PaToH: a multilevel hypergraph partitioning tool, version 3.0. Bilkent University, Department of Computer Engineering, Ankara, 06533 Turkey. PaToH is available at http://bmi.osu.edu/~umit/software.htm

  8. Çatalyürek Ü, Aykanat C (2001) A hypergraph-partitioning approach for coarse-grain decomposition. In: SC2001, Denver, November 2001

    Google Scholar 

  9. Çatalyürek Ü, Aykanat C (1999) Hypergraph-partitioning based decomposition for parallel sparse-matrix vector multiplication. IEEE Trans Parallel Distrib Syst 10(7):673–693

    Article  Google Scholar 

  10. Caldwell AE, Kahng AB, Markov IL (2000) Improved algorithms for hypergraph bipartitioning. In: Proceedings of Asia and South Pacific design automation conference, pp 661–666

    Google Scholar 

  11. David R, Alla H (1987) Continuous Petri nets. In: Proceedings of the 8th European workshop on application and theory of Petri nets, Zaragoza, Spain, pp 275–294

    Google Scholar 

  12. David R, Alla H (1990) Autonomous and timed continuous Petri nets. In: Proceedings of 11th Int conference on application and theory of Petri nets, Paris, France, pp 367–381

    Google Scholar 

  13. Dijkstra EW (1971) Hierarchical ordering of sequential processes. Acta Inform 2:115–138

    Article  MathSciNet  Google Scholar 

  14. Ding Z (2009) Static analysis of concurrent programs using ordinary differential equations. Lect Notes Comput Sci 5684:1–35

    Article  Google Scholar 

  15. Ding Z, Shen H, Cao J (2011) Hypergraph partitioning for the parallel computation of continuous Petri nets. In: PaCT 2011, Kazan, Russia, pp 257–271

    Google Scholar 

  16. Dingle NJ, Harrison PG, Knottenbelt WJ (2004) Uniformization and hypergraph partitioning for the distributed computation of response time densities in very large Markov models. J Parallel Distrib Comput 64:908–920

    Article  MATH  Google Scholar 

  17. Duri S, Buy U, Devarapalli R, Shatz SM (1994) Application and experimental evaluation of state space reduction methods for deadlock analysis in Ada. ACM Trans Softw Eng Methodol 3(4):340–380

    Article  Google Scholar 

  18. Ehrig R, Nowak U, Deuflhard P (1998) Massively parallel linearly-implicit extrapolation algorithms as a powerful tool in process simulation. In: Parallel computing: fundamentals, applications and new directions. Elsevier, Amsterdam, pp 517–524

    Chapter  Google Scholar 

  19. Franklin MA (1978) Parallel solution of ordinary differential equations. IEEE Trans Comput 27(5):413–420

    Article  MATH  Google Scholar 

  20. Gear CW (1988) Parallel methods for ordinary differential equations. Calculo 1(2):1–20

    Article  Google Scholar 

  21. Hiraishi K (2008) Performance evaluation of workflows using continuous Petri nets with interval firing speeds. In: Petri Nnets’08. Lecture notes in computer science, vol 5062, pp 231–250

    Google Scholar 

  22. Helmbold D, Luckham D (1985) Debugging Ada tasking programs. IEEE Softw 2(2):47–57

    Article  Google Scholar 

  23. Hendrickson B, Kolda TG (2000) Graph partitioning models for parallel computing. Parallel Comput 26:1519–1534

    Article  MathSciNet  MATH  Google Scholar 

  24. Hendrickson B, Kolda TG (2000) Partitioning rectangular and structurally nonsymmetric sparse matrices for parallel computation. SIAM J Sci Comput 21(6):2048–2072

    Article  MathSciNet  MATH  Google Scholar 

  25. Hindmarsh AC, Brown PN, Grant KE, Lee SL, Serban R, Shumaker DE, Woodward CS (2005) SUNDIALS, suite of nonlinear and differential/algebraic equation solvers. ACM Trans Math Softw 31:363–396

    Article  MathSciNet  MATH  Google Scholar 

  26. Holt RC (1972) Some deadlock properties on computer systems. ACM Comput Surv 4(3):179–196

    Article  MathSciNet  Google Scholar 

  27. Karam GM, Buhr RJ (1990) Starvation and critical race analyzers for Ada. IEEE Trans Softw Eng 16(8):829–843

    Article  Google Scholar 

  28. van der Houwen PJ, Sommeijer BP (1990) Parallel iteration of high-order Runge-Kutta methods with stepsize control. J Comput Appl Math 29:111–127

    Article  MathSciNet  MATH  Google Scholar 

  29. Karypis G, Aggarwal R, Kumar V, Shekhar S (1997) Multilevel hypergraph partitioning: application in VLSI domain. In: Proceedings of 34th conference on design automation, pp 526–529

    Chapter  Google Scholar 

  30. Karypis G, Aggarwal R, Kumar V, Shekhar S (1999) Multilevel hypergraph partitioning: application in VLSI domain. IEEE Trans Very Large Scale Integr (VLSI) Syst 7(1):69–79

    Article  Google Scholar 

  31. Karypis G, Kumar V (1998) Multilevel k-way partitioning scheme for irregular graphs. J Parallel Distrib Comput 48(1):96–129

    Article  MathSciNet  Google Scholar 

  32. Lengauer T (1990) Combinatorial algorithms for integrated circuit layout. Wiley, New York

    MATH  Google Scholar 

  33. Rao PS, Mouney G (1997) Data communication in parallel block predictor-corrector methods for solving ODE’s. Parallel Comput 23:1877–1888

    Article  MATH  Google Scholar 

  34. Silva M, Recalde L (2005) Continuization of timed Petri nets: from performance evaluation to observation and control. In: ICATPN’05. Lecture notes in computer science, vol 3536, pp 26–47

    Google Scholar 

  35. Vastenhouw B, Bisseling RH (2005) A two-dimensional data distribution method for parallel sparse matrix-vector multiplication. SIAM Rev 47(1):67–95

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center of Math Computing and Software Engineering, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Zuohua Ding & Hui Shen

  2. Institute of Software, Chinese Academy Sciences, Beijing, 100080, China

    Jianwen Cao

Authors
  1. Zuohua Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hui Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianwen Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zuohua Ding.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ding, Z., Shen, H. & Cao, J. Parallel computation of continuous Petri nets based on hypergraph partitioning. J Supercomput 62, 345–377 (2012). https://doi.org/10.1007/s11227-011-0724-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11227-011-0724-z

Keywords

Search

Navigation