The complexity of colouring problems on dense graphs
Theoretical Computer Science
A randomised 3-colouring algorithm
Discrete Mathematics - Graph colouring and variations
A randomised heuristical algorithm for estimating the chromatic number of a graph
Information Processing Letters
A randomized algorithm for k-colorability
Discrete Mathematics
Analysis of the mean field annealing algorithm for graph colouring
Journal of Artificial Neural Networks - Special issue: neural networks for optimization
Bitstream neurons for graph colouring
Journal of Artificial Neural Networks - Special issue: neural networks for optimization
Adapting the energy landscape for MFA
Journal of Artificial Neural Networks - Special issue: neural networks for optimization
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
The Complexity of Near-Optimal Graph Coloring
Journal of the ACM (JACM)
Graph coloring conditions for the existence of solutions to the timetable problem
Communications of the ACM
Graph Coloring with Adaptive Evolutionary Algorithms
Journal of Heuristics
A Survey of Automated Timetabling
Artificial Intelligence Review
Recent Developments in Practical Examination Timetabling
Selected papers from the First International Conference on Practice and Theory of Automated Timetabling
A Grouping Genetic Algorithm for Graph Colouring and Exam Timetabling
PATAT '00 Selected papers from the Third International Conference on Practice and Theory of Automated Timetabling III
A multistage evolutionary algorithm for the timetable problem
IEEE Transactions on Evolutionary Computation
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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.