Solving various weighted matching problems with constraints

  • Yves Caseau
  • François Laburthe
Session 1
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1330)


This paper studies the resolution of (augmented) weighted matching problems within a constraint programming framework. The first contribution of the paper is a set of branch-and-bound techniques that improves substantially the performance of algorithms based on constraint propagation and the second contribution is the introduction of weighted matching as a global constraint (MinWeightAIIDifferent), that can be propagated using specialized incremental algorithms from Operations Research. We first compare programming techniques that use constraint propagation with specialized algorithms from Operations Research, such as the Busaker and Gowen flow algorithm or the Hungarian method. Although CLP is shown not to be competitive with specialized polynomial algorithms for “pure” matching problems, the situation is different as soon as the problems are modified with additional constraints. Using the previously mentioned set of techniques, a simpler branch-and-bound algorithm based on constraint propagation can outperform a complex specialized algorithm. These techniques have been applied with success to the Traveling Salesman Problems [CL 97], which can be seen as an augmented matching problem. We also show that an incremental version of the Hungarian method can be used to propagate a weighted matching MinWeightAllDifferent constraint. This is an extension to the weighted case of the work of Régin [Ré 94], which we show to bring significant improvements on a timetabling example.


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  1. [CGL93]
    Y. Caseau, P.-Y. Guillo, E. Levenez. A Deductive and Object-Oriented Approach to a Complex Scheduling Problem. Proc. of DOOD'93, Phoenix, 1993.Google Scholar
  2. [CL94]
    Y. Caseau, F. Laburthe. Improved CLP Scheduling with Tasks Intervals. Proc. of the 11th International Conference on Logic Programming, P. Van Hentenryck ed., The MIT Press, 1994.Google Scholar
  3. [CL96]
    Y. Caseau, F. Laburthe. Cumulative Scheduling with Task Intervals. Proc. of the Joint International Conference and Symposium on Logic Programming, M. Maher ed., The MIT Press, 1996.Google Scholar
  4. [CL97]
    Y. Caseau, F. Laburthe. Solving small TSPs with Constraints. Proc. of the 14th International Conference on Logic Programming, L. Naish ed., The MIT Press, 1997.Google Scholar
  5. [CoL86]
    T. Cormen, C. Leiserson, R. Rivest. Introduction to Algorithms. The MIT Press, 1986Google Scholar
  6. [Ge 94]
    B. Gerards. Matching. in Handbook in Operations Research and Management Science (Networks) eds. M.O. Ball et al, 1994.Google Scholar
  7. [GM 79]
    M. Gondran, M. Minoux. Graphes and Algorithmes. Eyrolles, 1979 (french) and J. Wiley, 1984Google Scholar
  8. [GT 89]
    H.N. Gabow, R.E. Tarjan. Faster Scaling algorithms for network problems. SIAM Journal of Computing, 18, 1979Google Scholar
  9. [Jou 95]
    J. Jourdan. Concurrence et coopération de modèles multiples. Ph. D. Thesis, Paris VII University, 1995Google Scholar
  10. [Ma 77]
    A.K. Mackworth. Consistency in networks of relations. Artificial Intelligence, 8, 1977.Google Scholar
  11. [MM 88]
    R. Mohr, G. Massini. Running efficiently arc consistency, syntactic and structural pattern recognition. Springer Verlag, 1988Google Scholar
  12. [PS82]
    C. Papadimitrou, K. Steiglitz. Combinatorial Optimization. Prentice Hall, 1991Google Scholar
  13. [Ré 94]
    J.C. Régin. A Filtering Algorithm for Constraints of Difference in CSPs Proc. of AAAI, 1994.Google Scholar
  14. [Re 93]
    C. Reeves. Modern Heuristic techniques for combinatorial problems. Halsted Press, 1993.Google Scholar
  15. [VH 89]
    P. Van Hentenryck. Constraint satisfaction in Logic Programming. The MIT Press, 1989Google Scholar
  16. [VL 90]
    J. van Leuwen. Graph Algorithms. in Handbook of Theoretical Computer Science, Elsevier Science Publishers, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Yves Caseau
    • 1
  • François Laburthe
    • 2
  1. 1.Bouygues - Direction ScientifiqueSt Quentin en Yvelines cedex
  2. 2.Ecole Normale Supérieure D.M.I.Paris

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