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On the Inverse Shortest Paths Problem

In this paper we survey a variant of the inverse shortest paths problem. Given is a network in which certain node-pairs require connections over specific predefined single paths. The aim is to find link weights such that the desired paths are uniquely induced by a shortest-path algorithm. Further we require that the link weights fit existing shortest-path based routing protocols. We give a motivation for this problem, discuss a number of its solvability aspects, and show how a feasible solution can be obtained from its linear relaxation. A network operator who wants to obtain a specific routing pattern by adjusting link weights, will find practical use of the solution to the considered problem.