Recognizing Bundles in Time Table Graphs : a Structural Approach

Abstract

We are dealing with an application problem arising in a cooperation with the national German railway company which occurs in the analysis of time table data. The purpose is to infer the underlying railroad network and the actual travel route of the trains when only their time tables are known. The structural basis of our considerations in this paper is a directed graph constructed from train time tables, where train stations correspond to vertices, and where pairs of consecutive stops of trains correspond to edges. Determining the travel route of trains corresponds to an edge classification problem in this graph. Exploiting the structure of this graph, we approach the edge classification problem by locating vertices that intuitively correspond to train stations where the underlying railroad network branches into several directions, and that induce a partition of the edge set into bundles.We describe the modeling process of the classification problem resulting in the bundle recognition problem. Given the NP-hardness of the corresponding optimization problem, we present a heuristic that exploits among other things the geometry of the embedded directed graph. We perform a computational study using time table data from 13 European countries.