The Weighted Arborescence Constraint

  • Vinasetan Ratheil HoundjiEmail author
  • Pierre Schaus
  • Mahouton Norbert Hounkonnou
  • Laurence Wolsey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10335)


For a directed graph, a Minimum Weight Arborescence (MWA) rooted at a vertex r is a directed spanning tree rooted at r with the minimum total weight. We define the MinArborescence constraint to solve constrained arborescence problems (CAP) in Constraint Programming (CP). A filtering based on the LP reduced costs requires \(O(|V|^2)\) where |V| is the number of vertices. We propose a procedure to strengthen the quality of the LP reduced costs in some cases, also running in \(O(|V|^2)\). Computational results on a variant of CAP show that the additional filtering provided by the constraint reduces the size of the search tree substantially.


Directed Graph Leaf Node Search Tree Minimum Span Tree Travel Salesman Problem 
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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Vinasetan Ratheil Houndji
    • 1
    • 2
    Email author
  • Pierre Schaus
    • 1
  • Mahouton Norbert Hounkonnou
    • 2
  • Laurence Wolsey
    • 1
  1. 1.Université catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Université d’Abomey-CalaviAbomey-CalaviBenin

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