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The exact subgraph recoverable robust shortest path problem

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Passengers of a public transportation system are often forced to change their planned route due to deviation in travel times. Rerouting is mostly done by simple means such as announcements. We introduce a model, in which the passenger computes his optimal route on his mobile device in a given subnetwork according to the actual travel times. Those travel times are sent to him as soon as a delay occurs. The main focus of this paper is on the calculation of a small subnetwork. This subnetwork shall contain for every realization of travel times a shortest path of the original network and minimize the number of arcs. For this so called problem we introduce an approximation algorithm with an approximation factor of m/ℓ, for any fixed constant ℓ ∈ ℕ. This is the best possible approximation factor for the interval- and the Γ-scenario case, in which all realizations of travel times are given indirectly by lower and upper bounds on the arc cost. Unless P = NP, for those two scenario sets the problems is not approximable with a factor better than m (1-ε), where m is the number of arcs in the given graph and ε>0. © 2009 Springer-Verlag Berlin Heidelberg.




Büsing, C. (2009). The exact subgraph recoverable robust shortest path problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5868 LNCS, pp. 231–248).

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