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Using CP and ILP with tree decomposition to solve the sum colouring problem

Maël Minot 1 Samba Ndojh Ndiaye 1 Christine Solnon 1
1 M2DisCo - Geometry Processing and Constrained Optimization
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : The Minimum Sum Colouring Problem is an N P-hard problem derived from the well-known graph colouring problem. It consists in finding a proper colouring which minimizes the sum of the assigned colours rather than the number of those colours. This problem often arises in scheduling and resource allocation. Mainly incomplete approaches were proposed, but Integer Linear Programming (ILP) and Constraint Programming (CP) have also been used. In this paper, we conduct a more in-depth evaluation of ILP and CP's capabilities to solve the sum colouring problem, with several improvements. Moreover, we propose to combine ILP and CP in a tree decomposition with a bounded height.
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Submitted on : Wednesday, September 14, 2016 - 1:49:48 PM
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Maël Minot, Samba Ndojh Ndiaye, Christine Solnon. Using CP and ILP with tree decomposition to solve the sum colouring problem. Doctoral program of 22nd International Conference on Principles and Practice of Constraint Programming (CP 2016), Sep 2016, Toulouse, France. pp.1-10. ⟨hal-01366291⟩

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