Extended clique initialisation in examination timetabling

Many examination timetabling procedures employ a phased approach in which the first phase is often the allocation of a large set of mutually conflicting examinations which form a clique in the associated problem graph. The usual practice is to identify a single maximum clique, often quite arbitrarily, in this first phase. We show that in typical examination timetabling problems, unlike random graphs, there are often many alternative maximum cliques, and even larger dense subsets of nodes that are almost cliques. A number of methods are proposed for extending the scope of the clique initialisation to include a larger subset of examinations by considering sub-maximum cliques and/or quasi-cliques.