A shortest path problem or the way of the devils advocate
Transcription
A shortest path problem or the way of the devils advocate
A shortest path problem or the way of the devils advocate Birgit Engels1 and Gregor Pardella2 1 Arbeitsgruppe Faigle/Schrader (AFS) Institut für Informatik an der Universität zu Köln [email protected] 2 Institut für Informatik Universität zu Köln [email protected] 10. - 12. September 2009 We address a shortest path problem in a given uncapacited and undirected network N = (V, E) with positive edge costs. In addition we are given a single source-destination pair (s, t) s, t ∈ V , a shortest path πst connecting s and t and a new edge e = (p, q) ∈ E, 6∈ πst . The problem addressed now is to find a minimum set of edges Ec ⊆ E and the minimum weight increases for each edge ec ∈ Ec such that the shortest path πst between s and t traverses edge e. p q πst s t Ec? We show that this easy to state problem is NP-hard, give a heuristic for the problem and eventually an outlook on possible approximation strategies.