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In this paper a greedy algorithm to detect conflict cliques in intervalgraphs and circular-arc graphs is analyzed. In a graph, a stable set requiresthat at most one vertex is chosen for each edge. It is equivalent to requiringthat at most one vertex for each maximal clique is chosen. We show that thisalgorithm finds all maximal cliques for interval graphs, i.e. it can computethe convex hull of the stable set polytope. In case of circular-arc graphs, thealgorithm is not able to detect all maximal cliques, yet remaining correct.This problem occurs in the context of railway scheduling. A train requests theallocation of a railway infrastructure resource for a specific time interval.As one is looking for conflict-free train schedules, the used resourceallocation intervals in a schedule must not overlap. The conflict-free choicesof used intervals for each resource correspond to stable sets in the intervalgraph associated to the allocation time intervals.

Performance of a greedy algorithm for edge covering by cliques in interval graphs