On a Clique-Based Integer Programming Formulation of Vertex Colouring with Applications in Course Timetabling
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.
Cite
@article{arxiv.0710.3603,
title = {On a Clique-Based Integer Programming Formulation of Vertex Colouring with Applications in Course Timetabling},
author = {Edmund K. Burke and Jakub Marecek and Andrew J. Parkes and Hana Rudova},
journal= {arXiv preprint arXiv:0710.3603},
year = {2014}
}