Graph Properties Based Filtering

  • Nicolas Beldiceanu
  • Mats Carlsson
  • Sophie Demassey
  • Thierry Petit
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4204)


This article presents a generic filtering scheme, based on the graph description of global constraints. This description is defined by a network of binary constraints and a list of elementary graph properties: each solution of the global constraint corresponds to a subgraph of the initial network, retaining only the satisfied binary constraints, and which fulfills all the graph properties. The graph-based filtering identifies the arcs of the network that belong or not to the solution subgraphs. The objective is to build, besides a catalog of global constraints, also a list of systematic filtering rules based on a limited set of graph properties. We illustrate this principle on some common graph properties and provide computational experiments of the effective filtering on the group constraint.


Constraint Programming Global Constraint Maximum Match Graph Property Graph Class 
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  1. 1.
    Beldiceanu, N., Carlsson, M., Demassey, S., Petit, T.: Graph properties based filtering. Technical report, Swedish Institute of Computer Science, SICS T2006-10 (2006)Google Scholar
  2. 2.
    Beldiceanu, N., Carlsson, M., Petit, T.: Deriving filtering algorithms from constraint checkers. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 107–122. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Beldiceanu, N., Carlsson, M., Rampon, J.-X.: Global constraint catalog. Technical Report T2005-06, Swedish Institute of Computer Science (2005)Google Scholar
  4. 4.
    Beldiceanu, N., Carlsson, M., Rampon, J.-X., Truchet, C.: Graph invariants as necessary conditions for global constraints. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 92–106. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Beldiceanu, N., Katriel, I., Lorca, X.: Undirected forest constraints. In: Beck, J.C., Smith, B.M. (eds.) CPAIOR 2006. LNCS, vol. 3990, pp. 29–43. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Beldiceanu, N., Petit, T., Rochart, G.: Bounds of Graph Characteristics. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 742–746. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Bessière, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T.: Among, common and disjoint constraints. In: Hnich, B., Carlsson, M., Fages, F., Rossi, F. (eds.) CSCLP 2005. LNCS, vol. 3978, pp. 29–43. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    COSYTEC. CHIP Reference Manual, release 5.1 edition (1997)Google Scholar
  9. 9.
    Dooms, G., Deville, Y., Dupont, P.E.: CP(Graph): Introducing a graph computation domain in constraint programming. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 211–225. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness. W.H.Freeman and co., San Francisco (1979)MATHGoogle Scholar
  11. 11.
    Martin, P., Shmoys, D.B.: A New Approach to Computing Optimal Schedules for the Job-Shop Scheduling Problem. In: Cunningham, W.H., Queyranne, M., McCormick, S.T. (eds.) IPCO 1996. LNCS, vol. 1084, pp. 389–403. Springer, Heidelberg (1996)Google Scholar
  12. 12.
    Micali, S., Vazirani, V.V.: An \(\mathcal{O}(\sqrt{|V|} \cdot |{E}|)\) algorithm for finding maximum matching in general graphs. In: FOCS 1980, New York, pp. 17–27. IEEE, Los Alamitos (1980)Google Scholar
  13. 13.
    Pesant, G.: A filtering algorithm for the stretch constraint. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 183–195. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Régin, J.-C.: The Symmetric alldiff Constraint. In: 16th Int. Joint Conf. on Artificial Intelligence (IJCAI 99), pp. 420–425 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nicolas Beldiceanu
    • 1
  • Mats Carlsson
    • 2
  • Sophie Demassey
    • 1
  • Thierry Petit
    • 1
  1. 1.École des Mines de Nantes, LINA FRE CNRS 2729NantesFrance
  2. 2.SICSKistaSweden

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