TY - GEN A1 - Schwartz, Stephan A1 - Borndörfer, Ralf A1 - Bartz, Gerald T1 - The Graph Segmentation Problem N2 - We investigate a graph theoretical problem arising in the automatic billing of a network toll. Given a network and a family of user paths, we study the graph segmentation problem (GSP) to cover parts of the user paths by a set of disjoint segments. The GSP is shown to be NP-hard but for special cases it can be solved in polynomial time. We also show that the marginal utility of a segment is bounded. Computational results for real-world instances show that in practice the problem is more amenable than the theoretic bounds suggest. T3 - ZIB-Report - 16-53 KW - toll billing KW - graph segmentation KW - combinatorial optimization Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-60750 SN - 1438-0064 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Schwartz, Stephan A1 - Bartz, Gerald T1 - The Graph Segmentation Problem T2 - INOC 2017 – 8th International Network Optimization Conference N2 - We investigate a graph theoretical problem arising in the automatic billing of a network toll. Given a network and a family of user paths, we study the graph segmentation problem (GSP) to cover parts of the user paths by a set of disjoint segments. The GSP is shown to be NP-hard but for special cases it can be solved in polynomial time. We also show that the marginal utility of a segment is bounded. Computational results for real-world instances show that in practice the problem is more amenable than the theoretic bounds suggest. Y1 - 2018 VL - 64 SP - 35 EP - 44 ER -