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Combining Tree Partitioning, Precedence, and Incomparability Constraints

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Abstract

The tree constraint partitions a directed graph into node-disjoint trees. In many practical applications that involve such a partition, there exist side constraints specifying requirements on tree count, node degrees, or precedences and incomparabilities within node subsets. We present a generalisation of the tree constraint that incorporates such side constraints. The key point of our approach is to take partially into account the strong interactions between the tree partitioning problem and all the side constraints, in order to avoid thrashing during search. We describe filtering rules for this extended tree constraint and evaluate its effectiveness on three applications: the Hamiltonian path problem, the ordered disjoint paths problem, and the phylogenetic supertree problem.

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Authors and Affiliations

  1. École des Mines de Nantes, LINA FREE CNRS 2729, 44307, Nantes Cedex 3, France

    Nicolas Beldiceanu & Xavier Lorca

  2. Department of Information Technology, and The Linnaeus Centre for Bioinformatics, Uppsala University, Box 337, 751 05, Uppsala, Sweden

    Pierre Flener

Authors
  1. Nicolas Beldiceanu
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  2. Pierre Flener
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  3. Xavier Lorca
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Corresponding author

Correspondence to Pierre Flener.

Additional information

Some of this work was done while the second author was Visiting Faculty Member and Erasmus Exchange Teacher at Sabancı University in İstanbul, Turkey, during the academic year 2006/2007.

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Beldiceanu, N., Flener, P. & Lorca, X. Combining Tree Partitioning, Precedence, and Incomparability Constraints. Constraints 13, 459–489 (2008). https://doi.org/10.1007/s10601-007-9040-x

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