On the PROBABILISTIC MIN SPANNING TREE problem

Nicolas Boria (1, 2) , Cecile Murat (2) , Vangelis Paschos (2)

1 DAUIN - Department of Computer Engineering
2 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

We study a probabilistic optimization model for MIN SPANNING TREE PROBLEM, where any vertex vi of the input-graph G(V,E) has some presence probability pi in the final instance G′ ⊂ G that will effectively be optimized. Suppose that when this "real" instance G′ becomes known, a spanning tree T, called anticipatory or a priori spanning tree, has already been computed in G and one can run a quick algorithm (quicker than one that recomputes from scratch), called modification strategy, that modifies the anticipatory tree T in order to fit G′. The goal is to compute an anticipatory spanning tree of G such that, its modification for any G′ ⊆ G is optimal for G′. This is what we call PROBALISTIC MIN SPANNING TREE PROBLEM. In this paper we study complexity and approximation of PROBALISTIC MIN SPANNING TREE PROBLEM in complete graphs under two distinct modification strategies leading to different complexity results for the problem. For the first of the strategies developed, we also study two natural subproblems of PROBALISTIC MIN SPANNING TREE PROBLEM, namely, the PROBALISTIC METRIC MIN SPANNING TREE PROBLEM and the PROBALISTIC MIN SPANNING TREE PROBLEM 1,2 that deal with metric complete graphs and complete graphs with edge-weights either 1, or 2, respectively.

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

Nicolas Boria, Cecile Murat, Vangelis Paschos. On the PROBABILISTIC MIN SPANNING TREE problem. 2011. ⟨hal-00875638⟩