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Graph Colouring by Maximal Evidence Edge Adding

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Practice and Theory of Automated Timetabling III (PATAT 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2079))

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Abstract

Graph colouring is one of the most studied NP-hard problems. Many problems of practical interest can be modelled as colouring problems. The basic colouring problem is to group items in as few groups as possible, subject to the constraint that no incompatible items end up in the same group. Classical examples of applications include timetabling and scheduling [25]. We describe an iterative heuristic algorithm for adding new edges to a graph in order to make the search for a colouring easier. The heuristic is used to decide which edges should be added by sampling a number of approximate colourings and adding edges which have fewest conflicts with the generated colourings. We perform some analysis of the number of approximate colourings that might be needed to give good bounds on the probability of including an edge which increases the chromatic number of the graph. Experimental results on a set of “difficult graphs” arising from scheduling problems are given.

Work supported by a British Council Exchange Grant with Slovenia, ALIS No. 27

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Author information

Authors and Affiliations

  1. Department of Computer Science, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK

    Barry Rising

  2. Department of Theoretical Computer Science, Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia and IMFM, Jadranska 19, Ljubljana, Slovenia

    John Shawe-Taylor & Janez Žerovnik

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  1. Barry Rising
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  2. John Shawe-Taylor
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  3. Janez Žerovnik
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Editor information

Editors and Affiliations

  1. School of Computer Science and Information Technology Automated Scheduling, Optimisation and Planning Research Group, University of Nottingham, Jubilee Campus,Wollaton Road, NG8 1BB, Nottingham, UK

    Edmund Burke

  2. Department of Computer Science, FH Konstanz, University of Applied Science, Brauneggerstr. 55, 78462, Konstanz, Germany

    Wilhelm Erben

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© 2001 Springer-Verlag Berlin Heidelberg

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Rising, B., Shawe-Taylor, J., Žerovnik, J. (2001). Graph Colouring by Maximal Evidence Edge Adding. In: Burke, E., Erben, W. (eds) Practice and Theory of Automated Timetabling III. PATAT 2000. Lecture Notes in Computer Science, vol 2079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44629-X_18

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  • DOI: https://doi.org/10.1007/3-540-44629-X_18

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  • Print ISBN: 978-3-540-42421-5

  • Online ISBN: 978-3-540-44629-3

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