Simple and fast reoptimizations for the Steiner tree problem

Bruno Escoffier (1) , Martin Milanic (2) , Vangelis Paschos (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 RUTCOR - Rutgers Center for Operations Research

We address reoptimization issues for the Steiner tree problem. We assume that an optimal solution is given for some instance of the problem and the objective is to maintain a good solution when the instance is subject to minor modifications, the simplest such modifications being vertex insertions and deletions. We propose fast reoptimization strategies for the case of vertex insertions and we show that maintenance of a good solution for the "shrunk" instance, without ex nihilo computation, is impossible when vertex deletions occur. We also provide lower bounds for the approximation ratios of the reoptimization strategies studied.

Mots clés: approximation algorithms; reoptimization; Steiner tree

Domaines: Algorithme et structure de données [cs.DS]; Complexité [cs.CC]; Recherche opérationnelle [math.OC]

Bruno Escoffier, Martin Milanic, Vangelis Paschos. Simple and fast reoptimizations for the Steiner tree problem. 2007. ⟨hal-00948864⟩