A robust 2-stage version for the STEINER TREE problem

Vangelis Th. Paschos (1) , Orestis Teletis (2) , Vassilis Zissimopoulos (2)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 DI NKUA - Department of Informatics and Telecomunications [Kapodistrian Univ]

In this paper we consider a robust version for STEINER TREE. Under it, the problem is defined in a two-stage setting over a complete weighted graph whose vertices are associated with a probability of presence in the second stage. A first-stage feasible solution on the input graph might become infeasible in the second stage, when certain vertices of the graph fail (with the specified probability). Therefore, a well defined modification strategy is devised which transforms a partial solution to a feasible second-stage solution. The objective is to devise an algorithm for the first-stage solution (sometimes called the a priori or anticipatory solution) so that the expected second-stage solution cost is minimized. An important feature of this framework is that the modification strategy is essentially a part of the problem, while algorithmic treatment is required in the construction of the anticipatory solution. We provide complexity and approximation results regarding a modification strategy based upon the well known depth-first-search algorithm.

Mots clés: Approximation; Complexity; Graph; Probabilistic optimization; Robustness; Steiner tree

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

Vangelis Th. Paschos, Orestis Teletis, Vassilis Zissimopoulos. A robust 2-stage version for the STEINER TREE problem. 2007. ⟨hal-00180537⟩