Abstract
The weighted spanning tree constraint, or wst-constraint, is defined on an edgeweighted graph G and a value K. It states that G admits a spanning tree with weight at most K [3, 4]. It can be applied to network design problems as well as routing problems, in which it serves as a relaxation. In this work, we assume that we can represent the mandatory and possible edges that can belong to a solution to the wst-constraint, e.g., using a subset-bound set variable as in [3].
This work was partially supported by the European Community’s 7th Framework Programme (FP7/2007-2013). It was started when L.-M. Rousseau and W.-J. van Hoeve were visiting the University of Nice-Sophia Antipolis (June/July 2009).
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References
Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press, Cambridge (1990)
Dixon, B., Rauch, M., Tarjan, R.: Verification and sensitivity analysis of minimum spanning trees in linear time. SIAM J. Comput. 21(6), 1184–1192 (1992)
Dooms, G., Katriel, I.: The “not-too-heavy spanning tree” constraint. In: Van Hentenryck, P., Wolsey, L.A. (eds.) CPAIOR 2007. LNCS, vol. 4510, pp. 59–70. Springer, Heidelberg (2007)
Régin, J.-C.: Simpler and Incremental Consistency Checking and Arc Consistency Filtering Algorithms for the Weighted Spanning Tree Constraint. In: Perron, L., Trick, M.A. (eds.) CPAIOR 2008. LNCS, vol. 5015, pp. 233–247. Springer, Heidelberg (2008)
Tarjan, R.E.: Applications of path compression on balanced trees. Journal of the ACM 26(4), 690–715 (1979)
Tarjan, R.E.: Efficiency of a good but not linear set union algorithm. Journal of the ACM 22, 215–225 (1975)
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Régin, JC., Rousseau, LM., Rueher, M., van Hoeve, WJ. (2010). The Weighted Spanning Tree Constraint Revisited. In: Lodi, A., Milano, M., Toth, P. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2010. Lecture Notes in Computer Science, vol 6140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13520-0_31
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DOI: https://doi.org/10.1007/978-3-642-13520-0_31
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