On-line computation and maximum-weighted hereditary subgraph problems

URL des Cahiers : https://halshs.archives-ouvertes.fr/CAHIERS-MSE Voir aussi l'article basé sur ce document de travail paru dans "International Symposium on Algorithms and Computation", ISAAC 2005: Algorithms and Computation pp 433-442Cahiers de la Maison des Sciences Economiques 2006.34 - ISSN 1624-0340In this paper, we study the on-line version of maximum-weighted hereditary subgraph problems. In our on-line model, the final instance-graph (which has n vertices) is revealed in t clusters, 2 ≤ t ≤ n. We first focus on the on-line version of the following problem: finding a maximum-weighted subgraph satisfying some hereditary property. Then, we deal with the particular case of the independent set. For all these problems, we are interested in two types of results: the competitivity ratio guaranteed by the on-line algorithm and hardness results that account for the difficulty of the problems and for the quality of algorithms developed to solve them.Dans ce document, nous commençons par étudier la version on-line du problème du sous-graphe héréditaire de poids maximum, WHG, ci-dessous défini : étant donné un graphe G et une propriété héréditaire, trouver un sous-graphe de G de poids maximum satisfaisant. Ensuite, nous étudierons le cas particulier du problème du stable pondéré. Dans notre modèle on-line, nous supposons que l'instance finale de taille n'est révélée en t étapes (ou paquets), 2 ≤ t ≤ n. Nous analysons le comportement des algorithmes on-line résolvant le problème WHG et déterminons des rapports compétitifs (résultats positifs) et des résultats négatifs. Ces derniers résultats rendent compte aussi bien de la difficulté du problème que de la qualité des algorithmes élaborés pour les résoudre

On-line computation and maximum-weighted hereditary subgraph problems

In this paper1 we study the on-line version of maximum-weighted hereditary subgraph problems. In our on-line model, the final instance (a graph with n vertices) is revealed in t clusters, 2 ≤ t ≤ n . We first focus on an on-line version of the maximumweighted hereditary subgraph problem. Then, we deal with the particular case of the independent set problem. We are interested in two types of results: the competitive ratio guaranteed by the on-line algorithm and hardness results that account for the difficulty of the problems and for the quality of algorithms developed to solve them

On-line computation and maximum-weighted hereditary subgraph problems.

In this paper, we study the on-line version of maximum-weighted hereditary subgraph problems. In our on-line model, the final instance-graph (which has n vertices) is revealed in t clusters, 2 £ t £ n. We first focus on the on-line version of the following problem : finding a maximum-weighted subgraph satisfying some hereditary property. Then, we deal with the particular case of the independent set. For all these problems, we are interested in two types of results : the competitivity ratio guaranteed by the on-line algorithm and hardness results that account for the difficulty of the problems and for the quality of algorithms developed to solve them.On-line algorithm, hereditary property, independent set, competitivity ratio.