Scalable Parallel Numerical CSP Solver

  • Daisuke Ishii
  • Kazuki Yoshizoe
  • Toyotaro Suzumura
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8656)


We present a parallel solver for numerical constraint satisfaction problems (NCSPs) that can scale on a number of cores. Our proposed method runs worker solvers on the available cores and simultaneously the workers cooperate for the search space distribution and balancing. In the experiments, we attained up to 119-fold speedup using 256 cores of a parallel computer.


Search Space Load Balance Parallel Method Initial Domain Speedup Ratio 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Benhamou, F., Goualard, F., Granvilliers, L., Puget, J.F.: Revising Hull and Box Consistency. In: Proc. of ICLP, pp. 230–244 (1999)Google Scholar
  2. 2.
    Bordeaux, L., Hamadi, Y., Samulowitz, H.: Experiments with Massively Parallel Constraint Solving. In: Proc. of IJCAI, pp. 443–448 (2006)Google Scholar
  3. 3.
    Caro, S., Chablat, D., Goldsztejn, A., Ishii, D., Jermann, C.: A branch and prune algorithm for the computation of generalized aspects of parallel robots. Artificial Intelligence 211, 34–50 (2014)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Charles, P., Grothoff, C., Saraswat, V.: X10: an object-oriented approach to non-uniform cluster computing. In: Proc. of OOPSLA, pp. 519–538 (2005)Google Scholar
  5. 5.
    Chu, G., Schulte, C., Stuckey, P.J.: Confidence-based work stealing in parallel constraint programming. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 226–241. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Ishii, D., Goldsztejn, A., Jermann, C.: Interval-based projection method for under-constrained numerical systems. Constraints Journal 17(4), 432–460 (2012)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Gent, I.P., Jefferson, C., Miguel, I., Moore, N.C.A., Nightingale, P., Prosser, P., Unsworth, C.: A Preliminary Review of Literature on Parallel Constraint Solving. In: Proc. of Workshop on Parallel Methods for Constraint Solving, p. 13 (2011)Google Scholar
  8. 8.
    Goldsztejn, A., Goualard, F.: Box consistency through adaptive shaving. In: Proc. of SAC, pp. 2049–2054 (2010)Google Scholar
  9. 9.
    Grama, A., Gupta, A., Karypis, G., Kumar, V.: Introduction to Parallel Computing. Addison Wesley (2003)Google Scholar
  10. 10.
    Granvilliers, L., Benhamou, F.: Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques. ACM Transactions on Mathematical Software 32(1), 138–156 (2006)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Granvilliers, L., Hains, G.: A conservative scheme for parallel interval narrowing. Information Processing Letters 74(3-4), 141–146 (2000)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Jaffar, J., Santosa, A., Yap, R., Zhu, K.: Scalable distributed depth-first search with greedy work stealing. In: Proc. of ICTAI, pp. 98–103 (2004)Google Scholar
  13. 13.
    Lüling, R., Monien, B., Reinefeld, A., Tschöke, S.: Mapping Tree-Structured Combinatorial Optimization Problems onto Parallel Computers. In: Ferreira, A., Pardalos, P. (eds.) SCOOP 1995. LNCS, vol. 1054, pp. 115–144. Springer, Heidelberg (1996)Google Scholar
  14. 14.
    Otten, L., Dechter, R.: Towards Parallel Search for Optimization in Graphical Models. In: Proc. of ISAIM (2010)Google Scholar
  15. 15.
    Schubert, T., Lewis, M., Becker, B.: PaMiraXT: Parallel SAT Solving with Threads and Message Passing. JSAT 6, 203–222 (2009)zbMATHGoogle Scholar
  16. 16.
    Schulte, C.: Parallel search made simple. In: Proc. of TRICS, pp. 41–57 (2000)Google Scholar
  17. 17.
    Van Hentenryck, P., McAllester, D., Kapur, D.: Solving Polynomial Systems Using a Branch and Prune Approach. SIAM Journal on Numerical Analysis 34(2), 797–827 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Xie, F., Davenport, A.: Massively Parallel Constraint Programming for Supercomputers: Challenges and Initial Results. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 334–338. Springer, Heidelberg (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Daisuke Ishii
    • 1
  • Kazuki Yoshizoe
    • 1
    • 2
  • Toyotaro Suzumura
    • 2
    • 3
  1. 1.Tokyo Institute of TechnologyTokyoJapan
  2. 2.Japan Science and Technology AgencyJapan
  3. 3.IBM ResearchDublinIreland

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