The robust shortest path and the single-source shortest path problems : interval data

Martha Salazar-Neumann (1)

1 SMG

We consider two robust deviation problems; the robust deviation version of the problem to find a path of minimum weight connecting two specified nodes 1 and m, (the robust deviation shortest path problem ) and the robust version of the problem to find shortest paths from a fixed node 1 and all the nodes of the graph (the robust deviation single-source shortest path problem ). We consider both of them on finite directed graphs where arcs lengths are interval numbers. We give sufficient conditions for an arc (k, r) to be always (for all realization of data) on an optimal solution (strictly strong arcs and T-strictly strong arcs resp.) and for an arc to be never on an optimal solution (non weak arcs and non T-weak arcs resp.). These entities can be used to preprocess a given graph with interval data prior to the solution of the robust problem. In [3] was shown that such preprocessing procedure is quite effective in reducing the time to compute the solution of the robust deviation path problem. Based on these results we present polynomial time recognition algorithms.

Mots clés: Minimax regret optimization; Robust shortest path problem; uncertainty modeling; arc problem

Domaines: Complexité [cs.CC]; Recherche opérationnelle [math.OC]

Martha Salazar-Neumann. The robust shortest path and the single-source shortest path problems : interval data. 2007. ⟨hal-00180624⟩