Contraction-Based Heuristics to Improve the Efficiency of Algorithms Solving the Graph Colouring Problem

Summary

Graph vertex colouring can be defined in such a way where colour assignments are substituted by vertex contractions. We present various hypergraph representations for the graph colouring problem all based on the approach where vertices are merged into groups. In this paper, we explain this approach and identify three reasons that make it useful. First, generally, this approach provides a potential decrease in computational complexity. Second, it provides a uniform and compact way in which algorithms, be it of a complete or a heuristic nature, can be defined and progress toward a colouring. Last, it opens the way to novel applications that extract information useful to guide algorithms during their search. These approaches can be useful in the design of an algorithm.