Abstract
The inverse shortest path routing problem is to decide if a set of tentative routing patterns is simultaneously realizable. A routing pattern is defined by its destination and two arc subsets of required shortest path arcs and prohibited non-shortest path arcs. A set of tentative routing patterns is simultaneously realizable if there is a cost vector such that for all routing patterns it holds that all shortest path arcs are in some shortest path and no non-shortest path arc is in any shortest path to the destination of the routing pattern. Our main result is that this problem is NP-complete, contrary to what has been claimed earlier in the literature. Inverse shortest path routing problems naturally arise as a subproblem in bilevel programs where the lower level consists of shortest path problems. Prominent applications that fit into this framework include traffic engineering in IP networks using OSPF or IS-IS and in Stackelberg network pricing games. In this paper we focus on the common subproblem that arises if the bilevel program is linearized and solved by branch-and-cut. Then, it must repeatedly be decided if a set of tentative routing patterns is realizable. In particular, an NP-completeness proof for this problem is given.
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Call, M., Holmberg, K. (2011). Complexity of Inverse Shortest Path Routing. In: Pahl, J., Reiners, T., Voß, S. (eds) Network Optimization. INOC 2011. Lecture Notes in Computer Science, vol 6701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21527-8_39
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DOI: https://doi.org/10.1007/978-3-642-21527-8_39
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