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arXiv · 0710.3603

On a Clique-Based Integer Programming Formulation of Vertex Colouring with Applications in Course Timetabling

Edmund K. Burke·Jakub Marecek·Andrew J. Parkes·Hana Rudova
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Abstract

Vertex colouring is a well-known problem in combinatorial optimisation, whose alternative integer programming formulations have recently attracted considerable attention. This paper briefly surveys seven known formulations of vertex colouring and introduces a formulation of vertex colouring using a suitable clique partition of the graph. This formulation is applicable in timetabling applications, where such a clique partition of the conflict graph is given implicitly. In contrast with some alternatives, the presented formulation can also be easily extended to accommodate complex performance indicators (``soft constraints'') imposed in a number of real-life course timetabling applications. Its performance depends on the quality of the clique partition, but encouraging empirical results for the Udine Course Timetabling problem are reported.

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Edmund K. Burke, Jakub Marecek, Andrew J. Parkes, Hana Rudova. 2009-07-07. On a Clique-Based Integer Programming Formulation of Vertex Colouring with Applications in Course Timetabling. https://doi.org/10.1007/s10479-010-0716-z

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