### Vertex Disjoint Paths for Dispatching in Railways

Holger Flier, MatÃºs MihalÃ¡K, Anita SchÃ¶Bel, Peter Widmayer & Anna Zych
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 routing-in-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...