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dc.contributor.authorBurke, Edmund-
dc.contributor.authorMaracek, Jakub-
dc.contributor.authorParkes, Andrew J-
dc.contributor.authorRudova, Hana-
dc.description.abstractFor many problems in scheduling and timetabling, the choice of a mathematical programming formulation is determined by the formulation of the graph colouring component. This paper briefly surveys seven known integer programming formulations of vertex colouring and introduces a new approach using "supernodes". In the definition of George and McIntyre (SIAM J. Numer. Anal. 15(1):90-112, 1978), a "supernode" is a complete subgraph, within which every pair of vertices have the same neighbourhood outside of the subgraph. A polynomial-time algorithm for obtaining the best possible partition of an arbitrary graph into supernodes is given. This makes it possible to use any formulation of vertex multicolouring to encode vertex colouring. Results of empirical tests on benchmark instances in graph colouring (DIMACS) and timetabling (Udine Course Timetabling) are also provided and discussed.en_UK
dc.relationBurke E, Maracek J, Parkes AJ & Rudova H (2010) A supernodal formulation of vertex colouring with applications in course timetabling, Annals of Operations Research, 179 (1), pp. 105-130.-
dc.rightsThe publisher does not allow this work to be made publicly available in this Repository. Please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study.-
dc.subjectVertex colouringen_UK
dc.subjectGraph colouringen_UK
dc.subjectInteger programmingen_UK
dc.titleA supernodal formulation of vertex colouring with applications in course timetablingen_UK
dc.typeJournal Articleen_UK
dc.rights.embargoreasonThe publisher does not allow this work to be made publicly available in this Repository therefore there is an embargo on the full text of the work.-
dc.citation.jtitleAnnals of Operations Research-
dc.type.statusPublisher version (final published refereed version)-
dc.contributor.affiliationComputing Science and Mathematics-
dc.contributor.affiliationUniversity of Nottingham-
dc.contributor.affiliationUniversity of Nottingham-
dc.contributor.affiliationMasaryk University-
Appears in Collections:Computing Science and Mathematics Journal Articles

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