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.