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Laboratoire d'informatique fondamentale de Marseille UMR 6166 - CNRS, Université de la Méditerranée, Université de Provence |
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Laboratoire d'informatique fondamentale de Marseille UMR 6166 - CNRS, Université de la Méditerranée, Université de Provence |
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| HAL : hal-00005260, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Algorithmica 33 (2002) 243-262 |
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| Augmenting trees to meet connectivity and diameter constraints |
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| Victor Chepoi 1Yann Vaxès 1 |
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| (2002) |
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| Given a graph G=(V,E) and a positive integer D, we consider the problem of finding a minimum number of new edges E' such that the augmented graph G'=(V,E\cup E') is biconnected and has diameter no greater than D. In this note we show that this problem is NP-hard for all fixed D, by employing a reduction from the DOMINATING SET problem. We prove that the problem remains NP-hard even for forests and trees, but in this case we present approximation algorithms with worst-case bounds 3 (for even D) and 6 (for odd D). A closely related problem of finding a minimum number of edges such that the augmented graph has diameter no greater than D has been shown to be NP-hard by Schoone, Bodlaender, and van Leeuwen, J. Graph Theory, 11 (1987) when D=3, and by Li, McCormick, and Simchi--Levi, Operations Research Letters, 11 (1991) when D=2. |
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| 1 : | Laboratoire d'informatique Fondamentale de Marseille (LIF) |
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CNRS : UMR6166 – Université de la Méditerranée - Aix-Marseille II – Université de Provence - Aix-Marseille I |
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| Domaine | : | Informatique/Algorithme et structure de données |
| hal-00005260, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00005260 | |
| oai:hal.archives-ouvertes.fr:hal-00005260 | |
| Contributeur : Yann Vaxès | |
| Soumis le : Jeudi 9 Juin 2005, 23:12:13 | |
| Dernière modification le : Jeudi 9 Juin 2005, 23:12:13 | |
