Finding Cliques of Maximum Weight on a Generalization of Permutation Graphs

We propose a dynamic programming procedure for computing the clique of maximum weight on a class of graphs arising in the solution of train timetabling problems. These graphs generalize, in two ways permutation graphs, defined as the intersection graphs of segments joining two parallel lines. First, two segments are joined by an edge not only if they intersect but also if their endpoints are sufficiently close. Second, two parallel segments may be joined by an edge even if they are arbitrarily far away from each other.