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Parallelizing Union-Find in Constraint Handling Rules Using Confluence Analysis

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Book cover Logic Programming (ICLP 2005)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 3668))

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Abstract

Constraint Handling Rules is a logical concurrent committed-choice rule-based language. Recently it was shown that the classical union-find algorithm can be implemented in CHR with optimal time complexity. Here we investigate if a parallel implementation of this algorithm is also possible in CHR. The problem is hard for several reasons:

- Up to now, no parallel computation model for CHR was defined.

- Tarjan’s optimal union-find is known to be hard to parallelize.

- The parallel code should be as close as possible to the sequential one.

It turns out that confluence analysis of the sequential implementation gives almost all the information needed to parallelize the union-find algorithm under a rather general parallel computation model for CHR.

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References

  1. Abdennadher, S.: Operational Semantics and Confluence of Constraint Propagation Rules. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  2. Abdennadher, S., Frühwirth, T., Holzbauz, C. (eds.): Special Issue on Constraint Handling Rules, Journal of Theory and Practice of Logic Programming (TPLP). Cambridge University Press (2005) (to appear)

    Google Scholar 

  3. Abdennadher, S., Frühwirth, T., Meuss, H.: Confluence and Semantics of Constraint Simplification Rules. Constraints Journal 4(2) (1999)

    Google Scholar 

  4. Anderson, R.J., Woll, H.: Wait-free parallel algorithms for the union-find problem. In: STOC 1991: Proceedings of the twenty-third annual ACM symposium on Theory of computing, Revision of November 1994, pp. 370–380. ACM Press, New York (1994)

    Google Scholar 

  5. Atallah, M.J., Goodrich, M.T., Kosaraju, S.R.: Parallel algorithms for evaluating sequences of set-manipulation operations. J. ACM 41(6), 1049–1088 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  6. Duck, G.J., Stuckey, P.J., de la Banda, M.G., Holzbaur, C.: The Refined Operational Semantics of Constraint Handling Rules. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 90–104. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  7. Frühwirth, T.: Theory and Practice of Constraint Handling Rules, Special Issue on Constraint Logic Programming. Journal of Logic Programming, 95–138 (October 1998)

    Google Scholar 

  8. Frühwirth, T., Abdennadher, S.: Essentials of Constraint Programming. Springer, Heidelberg (2003)

    Google Scholar 

  9. Galil, Z., Italiano, G.F.: Data Structures and Algorithms for Disjoint Set Union Problems. ACM Comp. Surveys 23(3), 319 (1991)

    Article  Google Scholar 

  10. Pinotti, M.C., Crupi, V.A., Das, S.K.: A parallel solution to the extended set union problem with unlimited backtracking. In: IPPS 1996: Proceedings of the 10th International Parallel Processing Symposium, Washington, DC, USA, pp. 182–186. IEEE Computer Society, Los Alamitos (1996)

    Google Scholar 

  11. Saraswat, V.A., Rinard, M.: Concurrent constraint programming. In: POPL 1990: Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pp. 232–245. ACM Press, New York (1990)

    Chapter  Google Scholar 

  12. Saraswat, V.A., Rinard, M., Panangaden, P.: The semantic foundations of concurrent constraint programming. In: POPL 1991: Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pp. 333–352. ACM Press, New York (1991)

    Chapter  Google Scholar 

  13. Schrijvers, T., Frühwirth, T.: Union-Find in CHR. Technical Report CW389, Department of Computer Science, K.U.Leuven, Belgium (July 2004)

    Google Scholar 

  14. Schrijvers, T., Frühwirth, T.: Analysing the CHR Implementation of Union-Find. In: 19th Workshop on (Constraint) Logic Programming (W(C)LP 2005), Ulmer Informatik-Berichte 2005-01, University of Ulm, Germany (February 2005)

    Google Scholar 

  15. Schrijvers, T., Frühwirth, T.: CHR Website (May 2005), www.cs.kuleuven.ac.be/~dtai/projects/CHR/

  16. Schrijvers, T., Frühwirth, T.: Optimal Union-Find in Constraint Handling Rules, Programming Pearl. Journal of Theory and Practice of Logic Programming (TPLP) ( to appear)

    Google Scholar 

  17. Tarjan, R.E., van Leeuwen, J.: Worst-case Analysis of Set Union Algorithms. J. ACM 31(2), 245–281 (1984)

    Article  MATH  MathSciNet  Google Scholar 

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Frühwirth, T. (2005). Parallelizing Union-Find in Constraint Handling Rules Using Confluence Analysis. In: Gabbrielli, M., Gupta, G. (eds) Logic Programming. ICLP 2005. Lecture Notes in Computer Science, vol 3668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11562931_11

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  • DOI: https://doi.org/10.1007/11562931_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29208-1

  • Online ISBN: 978-3-540-31947-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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