Improving Graph Colouring Algorithms and Heuristics Using a Novel Representation

Increasing the Efficiency of Graph Colouring Algorithms with a Representation Based on Vector Operations

We introduce a novel representation for the graph colouring problem, called the Integer Merge Model, which aims to reduce the time complexity of graph colouring algorithms. Moreover, this model provides useful information to aid in the creation of heuristics that can make the colouring process even faster. It also serves as a compact definition for the description of graph colouring algorithms....

Comparing the Best Maximum Clique Finding Algorithms, Which are Using Heuristic Vertex Colouring

In this paper two best known at the moment algorithms for finding the maximum clique is compared. A key technique that both algorithms rely on is using a heuristic vertex colouring. The only difference between those algorithms is a way of using vertex-colouring and this difference in the very important. The algorithms’ approaches are divided in this paper into two classes: reapplying vertex col...

Breaking the Symmetry of the Graph Colouring Problem with Genetic Algorithms

The graph colouring problem is a widely studied combinatorial optimisation problem with a highly symmetric solution space. Many heuristics and search algorithms are unattractive for general solution, i.e. they generate poor approximate solutions, because they were originally designed for specific problem instances. Population-based approaches like genetic algorithms do not provide a good altern...

Distributed asynchronous heuristics for graph colouring

Tackling the edge dynamic graph colouring problem with and without future adjacency information

Many real world operational research problems, such as frequency assignment and exam timetabling, can be reformulated as graph colouring problems (GCPs). Most algorithms for theGCPoperate under the assumption that its constraints are fixed, allowing us to model the problem using a static graph. However, in many real-world cases this does not hold and it is more appropriate to model problems wit...