An Integer Programming Algorithm for Routing Optimization in IP Networks
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Complexity of inverse shortest path routing
INOC'11 Proceedings of the 5th international conference on Network optimization
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We study the complexity of two inverse shortest paths (ISP)problems with integer arc lengths and the requirement for uniquelydetermined shortest paths. Given a collection of paths in adirected graph D = (V, A), the task is to findpositive integer arc lengths such that the given paths are uniquelydetermined shortest paths between their respective terminals. Inthe first problem we seek for arc lengths that minimize the lengthof the longest of the prescribed paths. In the second problem, thelength of the longest arc is to be minimized. We show that it is5©5«-hard to approximate the minimallongest path length within a factor less than 8-7 or the minimallongest arc length within a factor less than 9-8. This answers the(previously) open question whether these problems are5©5«-hard or not. We also present a simplealgorithm that achieves an 5ª(|V|)-approximationguarantee for both variants. Both ISP problems arise in theplanning of telecommunication networks with shortest path routingprotocols. Our results imply that it is5©5«-hard to decide whether a given pathset can be realized with a real shortest path routing protocol suchas OSPF, IS-IS, or RIP. © 2007 Wiley Periodicals, Inc.NETWORKS, Vol. 50(1), 2936 2007