Autonomous Agents and Multi-Agent Systems

, Volume 32, Issue 5, pp 569–601 | Cite as

A new distributed algorithm for efficient generalized arc-consistency propagation

  • Shufeng Kong
  • Jae Hee Lee
  • Sanjiang Li


Generalized arc-consistency propagation is predominantly used in constraint solvers to efficiently prune the search space when solving constraint satisfaction problems. Although many practical applications can be modelled as distributed constraint satisfaction problems, no distributed arc-consistency algorithms so far have considered the privacy of individual agents. In this paper, we propose a new distributed arc-consistency algorithm, called \(\mathsf {DisAC3.1}\), which leaks less private information of agents than existing distributed arc-consistency algorithms. In particular, \(\mathsf {DisAC3.1}\) uses a novel termination determination mechanism, which allows the agents to share domains, constraints and communication addresses only with relevant agents. We further extend \(\mathsf {DisAC3.1}\) to \(\mathsf {DisGAC3.1}\), which is the first distributed algorithm that enforces generalized arc-consistency on k-ary (\(k\ge 2\)) constraint satisfaction problems. Theoretical analyses show that our algorithms are efficient in both time and space. Experiments also demonstrate that \(\mathsf {DisAC3.1}\) outperforms the state-of-the-art distributed arc-consistency algorithm and that \(\mathsf {DisGAC3.1}\) ’s performance scales linearly in the number of agents.


Distributed constraint satisfaction problems Generalized arc-consistency Privacy Termination detection 



The authors sincerely thank the anonymous reviewers of Autonomous Agents and Multi-Agent Systems for their very helpful comments. The work of SL was partially supported by NSFC (No. 11671244), and the work of JL was partially supported by the Alexander von Humboldt Foundation.


  1. 1.
    Awerbuch, B., & Gallager, R. (1987). A new distributed algorithm to find breadth first search trees. IEEE Transactions on Information Theory, 33(3), 315–322.zbMATHGoogle Scholar
  2. 2.
    Baudot, B., & Deville, Y. (1997). Analysis of distributed arc-consistency algorithms. Technical report, Université catholique de Louvain.Google Scholar
  3. 3.
    Bessiere, C. (1994). Arc-consistency and arc-consistency again. Artificial Intelligence, 65(1), 179–190.MathSciNetGoogle Scholar
  4. 4.
    Bessiere, C., Freuder, E. C., & Régin, J. C. (1999). Using constraint metaknowledge to reduce arc consistency computation. Artificial Intelligence, 107(1), 125–148.MathSciNetzbMATHGoogle Scholar
  5. 5.
    Bessiere, C., Régin, J. C., Yap, R. H., & Zhang, Y. (2005). An optimal coarse-grained arc consistency algorithm. Artificial Intelligence, 165(2), 165–185.MathSciNetzbMATHGoogle Scholar
  6. 6.
    Boerkoel, J. C, Jr., & Durfee, E. H. (2013). Distributed reasoning for multiagent simple temporal problems. Journal of Artificial Intelligence Research, 47, 95–156.MathSciNetzbMATHGoogle Scholar
  7. 7.
    Chandy, K. M., & Misra, J. (1985). A paradigm for detecting quiescent properties in distributed computations. In K. R. Apt (Ed.), Logics and models of concurrent systems (pp. 325–341). New York: Springer.Google Scholar
  8. 8.
    Chandy, K. M., & Lamport, L. (1985). Distributed snapshots: Determining global states of distributed systems. ACM Transactions on Computer Systems (TOCS), 3(1), 63–75.Google Scholar
  9. 9.
    Chandy, K. M., & Misra, J. (1986). How processes learn. Distributed Computing, 1(1), 40–52.zbMATHGoogle Scholar
  10. 10.
    Chang, E. J. H. (1982). Echo algorithms: Depth parallel operations on general graphs. IEEE Transactions on Software Engineering, SE–8(4), 391–401.Google Scholar
  11. 11.
    Conry, S. E., Kuwabara, K., Lesser, V. R., & Meyer, R. A. (1991). Multistage negotiation for distributed constraint satisfaction. IEEE Transactions on Systems, Man, and Cybernetics, 21(6), 1462–1477.zbMATHGoogle Scholar
  12. 12.
    Cooper, P. R., & Swain, M. J. (1992). Arc consistency: Parallelism and domain dependence. Artificial Intelligence, 58(1–3), 207–235.MathSciNetGoogle Scholar
  13. 13.
    Dechter, R., Meiri, I., & Pearl, J. (1991). Temporal constraint networks. Artificial Intelligence, 49(1–3), 61–95.MathSciNetzbMATHGoogle Scholar
  14. 14.
    Dijkstra, E. W., Feijen, W. H., & Van Gasteren, A. M. (1986). Derivation of a termination detection algorithm for distributed computations. Information Processing Letters, 16(5), 217–219. Scholar
  15. 15.
    Dijkstra, E. W., & Scholten, C. S. (1980). Termination detection for diffusing computations. Information Processing Letters, 11(1), 1–4.MathSciNetzbMATHGoogle Scholar
  16. 16.
    Eriksen, O, & Skyum, S. (1985). Symmetric distributed termination. DAIMI report series 14(189).Google Scholar
  17. 17.
    Faltings, B., Léauté, T., & Petcu, A. (2008). Privacy guarantees through distributed constraint satisfaction. In 2008 IEEE/WIC/ACM international conference on web intelligence and intelligent agent technology (Vol. 2, pp. 350–358).Google Scholar
  18. 18.
    Grinshpoun, T. (2012). When you say (DCOP) privacy, what do you mean?—Categorization of DCOP privacy and insights on internal constraint privacy. In: J. Filipe, A. L. N. Fred (Eds.), ICAART 2012—Proceedings of the 4th international conference on agents and artificial intelligence (Vol. 1, pp. 380–386)—Artificial Intelligence, Vilamoura, Algarve, Portugal, 6–8 February, 2012. SciTePress.Google Scholar
  19. 19.
    Grinshpoun, T., & Tassa, T. (2016). P-syncbb: A privacy preserving branch and bound dcop algorithm. Journal of Artificial Intelligence Research, 57(1), 621–660.MathSciNetzbMATHGoogle Scholar
  20. 20.
    Gu, J., Sosic, R. (1991). A parallel architecture for constraint satisfaction. In: International conference on industrial and engineering applications of artificial intelligence and expert systems (pp. 229–237).Google Scholar
  21. 21.
    Hamadi, Y. (2002). Optimal distributed arc-consistency. Constraints, 7(3–4), 367–385.MathSciNetzbMATHGoogle Scholar
  22. 22.
    Hassine, A. B., & Ghedira, K. (2002). How to establish arc-consistency by reactive agents. In Proceedings of the 15th European conference on artificial intelligence (pp. 156–160).Google Scholar
  23. 23.
    Hassine, A. B., Ghedira, K., & Ho, T. B. (2004). New distributed filtering-consistency approach to general networks. In Proceedings of the 17th international conference on industrial and engineering applications of artificial intelligence and expert systems (pp. 708–717).Google Scholar
  24. 24.
    Huang, S. T. (1989). Detecting termination of distributed computations by external agents. In Proceedings of the 9th international conference on distributed computing systems (pp. 79–84).Google Scholar
  25. 25.
    Hubbe, P. D., & Freuder, E. C. (1992). An efficient cross product representation of the constraint satisfaction problem search space. In Proceedings of the tenth national conference on artificial intelligence (pp. 421–427).Google Scholar
  26. 26.
    Huffman, D. A. (1971). Impossible objects as nonsense sentences. Machine Intelligence, 6(1), 295–323.Google Scholar
  27. 27.
    Huhns, M. N., & Bridgeland, D. M. (1991). Multiagent truth maintenance. IEEE Transactions on Systems, Man, and Cybernetics, 21(6), 1437–1445.Google Scholar
  28. 28.
    Kong, S., Lee, J. H., & Li, S. (2018). Multiagent simple temporal problem: The Arc-consistency approach. In Thirty-Second AAAI Conference on Artificial Intelligence, AAAI’18. AAAI Press.Google Scholar
  29. 29.
    Lai, T. H., & Wu, L. F. (1995). An (n -1)-resilient algorithm for distributed termination detection. IEEE Transactions on Parallel and Distributed Systems, 6(1), 63–78.Google Scholar
  30. 30.
    Léauté, T., & Faltings, B. (2013). Protecting privacy through distributed computation in multi-agent decision making. Journal of Artificial Intelligence Research, 47, 649–695.MathSciNetzbMATHGoogle Scholar
  31. 31.
    Li, S., Liu, W., & Wang, S. (2013). Qualitative constraint satisfaction problems: An extended framework with landmarks. Artificial Intelligence, 201, 32–58.MathSciNetzbMATHGoogle Scholar
  32. 32.
    Lynch, N. A. (1996). Distributed algorithms. Burlington: Morgan Kaufmann.zbMATHGoogle Scholar
  33. 33.
    Mackworth, A. K. (1977). Consistency in networks of relations. Artificial Intelligence, 8(1), 99–118.MathSciNetzbMATHGoogle Scholar
  34. 34.
    Maheswaran, R. T., Pearce, J. P., Bowring, E., Varakantham, P., & Tambe, M. (2006). Privacy loss in distributed constraint reasoning: A quantitative framework for analysis and its applications. Autonomous Agents and Multi-Agent Systems, 13(1), 27–60.Google Scholar
  35. 35.
    Maruyama, H. (1990). Structural disambiguation with constraint propagation. In ACL (pp. 31–38).Google Scholar
  36. 36.
    Mason, C. L., & Johnson, R. R. (1988). Datms: A framework for distributed assumption based reasoning. Technical report, Lawrence Livermore National Lab., CA (USA).Google Scholar
  37. 37.
    Matocha, J., & Camp, T. (1998). A taxonomy of distributed termination detection algorithms. Journal of Systems and Software, 43(3), 207–221.Google Scholar
  38. 38.
    Mattern, F. (1987). Algorithms for distributed termination detection. Distributed Computing, 2(3), 161–175.Google Scholar
  39. 39.
    Mayo, J., & Kearns, P. (1994). Distributed termination detection with roughly synchronized clocks. Information Processing Letters, 52(2), 105–108.Google Scholar
  40. 40.
    Meisels, A., & Zivan, R. (2007). Asynchronous forward-checking for discsps. Constraints, 12(1), 131–150.MathSciNetzbMATHGoogle Scholar
  41. 41.
    Mohr, R., & Henderson, T. C. (1986). Arc and path consistency revisited. Artificial Intelligence, 28(2), 225–233.Google Scholar
  42. 42.
    Montanari, U. (1974). Networks of constraints: Fundamental properties and applications to picture processing. Information Sciences, 7, 95–132.MathSciNetzbMATHGoogle Scholar
  43. 43.
    Nguyen, T., & Deville, Y. (1998). A distributed arc-consistency algorithm. Science of Computer Programming, 30(1–2), 227–250.MathSciNetzbMATHGoogle Scholar
  44. 44.
    Raynal, M. (2013). Distributed termination detection. In Distributed algorithms for message-passing systems (pp. 367–399). Berlin: Springer.Google Scholar
  45. 45.
    Samal, A., & Henderson, T. (1987). Parallel consistent labeling algorithms. International Journal of Parallel Programming, 16(5), 341–364.MathSciNetzbMATHGoogle Scholar
  46. 46.
    Savaux, J., Vion, J., Piechowiak, S., Mandiau, R., Matsui, T., Hirayama, K., Yokoo, M., Elmane, S., & Silaghi, M. (2016). DisCSPs with privacy recast as planning problems for self-interested agents. In 2016 IEEE/WIC/ACM international conference on web intelligence (WI) (pp. 359–366).Google Scholar
  47. 47.
    Shavit, N., & Francez, N. (1986) A new approach to detection of locally indicative stability. In International colloquium on automata, languages, and programming (pp. 344–358). Springer.Google Scholar
  48. 48.
    Silaghi, M. (2002). A comparison of distributed constraint satisfaction approaches with respect to privacy. In In DCR. Citeseer.Google Scholar
  49. 49.
    Sultanik, E. A., Lass, R. N., & Regli, W .C. (2007). Dcopolis: A framework for simulating and deploying distributed constraint optimization algorithms. In Proceedings of the workshop on distributed constraint reasoning.Google Scholar
  50. 50.
    Sycara, K., Roth, S. F., Sadeh, N., & Fox, M. S. (1991). Distributed constrained heuristic search. IEEE Transactions on Systems, Man, and Cybernetics, 21(6), 1446–1461.Google Scholar
  51. 51.
    Topor, R. W. (1984). Termination detection for distributed computations. Information Processing Letters, 18(1), 33–36.Google Scholar
  52. 52.
    Venkatesan, S. (1989). Reliable protocols for distributed termination detection. IEEE Transactions on Reliability, 38(1), 103–110.Google Scholar
  53. 53.
    Wallace, R. J., & Freuder, E. C. (2005). Constraint-based reasoning and privacy/efficiency tradeoffs in multi-agent problem solving. Artificial Intelligence, 161(1), 209–227.MathSciNetzbMATHGoogle Scholar
  54. 54.
    Yokoo, M., Durfee, E. H., Ishida, T., & Kuwabara, K. (1998). The distributed constraint satisfaction problem: Formalization and algorithms. IEEE Transactions on Knowledge and Data Engineering, 10(5), 673–685.Google Scholar
  55. 55.
    Yokoo, M., & Hirayama, K. (2000). Algorithms for distributed constraint satisfaction: A review. Autonomous Agents and Multi-Agent Systems, 3(2), 185–207.Google Scholar
  56. 56.
    Yokoo, M., Suzuki, K., & Hirayama, K. (2005). Secure distributed constraint satisfaction: Reaching agreement without revealing private information. Artificial Intelligence, 161(1), 229–245.MathSciNetzbMATHGoogle Scholar
  57. 57.
    Zhang, Y., & Mackworth, A. K. (1991). Parallel and distributed algorithms for finite constraint satisfaction problems. In Proceedings of the 3th IEEE symposium on parallel and distributed processing (pp. 394–397).Google Scholar
  58. 58.
    Zhang, Y., & Yap, R. H. C. (2001). Making ac-3 an optimal algorithm. In Proceedings of the 17th international joint conference on artificial intelligence (pp. 316–321).Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Centre for Quantum Software and Information, FEITUniversity of Technology SydneyUltimoAustralia
  2. 2.UTS-AMSS Joint Research Laboratory, AMSSChinese Academy of SciencesBeijingChina

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