Vertex Disjoint Paths for Dispatching in Railways

We study variants of the vertex disjoint paths problem in planar graphs where paths have to be selected from a given set of paths. We study the problem as a decision, maximization, and routingin-rounds problem. Although all considered variants are NP-hard in planar graphs, restrictions on the location of the terminals, motivated by railway applications, lead to polynomially solvable cases for the decision and maximization versions of the problem, and to a p-approximation algorithm for the routing-in-rounds problem, where p is the maximum number of alternative paths for a terminal pair. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems—Routing and layout, G.2.2 Graph Theory—Path and circuit problems, G.2.3 Applications