UnivTrevesV1, Main, Exploration, bibRecord, 000653

Exact and Parameterized Algorithms for MAX INTERNAL SPANNING TREE

Identifieur interne : 000653 ( Main/Exploration ); précédent : 000652; suivant : 000654

Exact and Parameterized Algorithms for MAX INTERNAL SPANNING TREE

Auteurs : Daniel Binkele-Raible [Allemagne] ; Henning Fernau [Allemagne] ; Serge Gaspers [Autriche] ; Mathieu Liedloff [France]

Source :

Algorithmica [ 0178-4617 ] ; 2013.

RBID : Pascal:13-0121992

Descripteurs français

Pascal (Inist)
- Routage, Compilation, Complexité temps, Chemin hamiltonien, Ramification, Identificateur, Arbre maximal, Problème NP difficile, Programmation dynamique, Degré graphe, Algorithmique, Analyse algorithme, ., Temps exponentiel.

English descriptors

KwdEn :
- Algorithm analysis, Algorithmics, Branching, Compilation, Dynamic programming, Exponential time, Graph degree, Hamiltonian path, Identifier, NP hard problem, Routing, Spanning tree, Time complexity.

Abstract

We consider the NP-hard problem of finding a spanning tree with a maximum number of internal vertices. This problem is a generalization of the famous HAMILTONIAN PATH problem. Our dynamic-programming algorithms for general and degree-bounded graphs have running times of the form O^*(cⁿ) with c ≤ 2. For graphs with bounded degree, c < 2. The main result, however, is a branching algorithm for graphs with maximum degree three. It only needs polynomial space and has a running time of O(1.8612ⁿ) when analyzed with respect to the number of vertices. We also show that its running time is 2.1364^kn^O(1) when the goal is to find a spanning tree with at least k internal vertices. Both running time bounds are obtained via a Measure & Conquer analysis, the latter one being a novel use of this kind of analysis for parameterized algorithms.

Affiliations:

Links toward previous steps (curation, corpus...)

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Le document en format XML

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<front><div type="abstract" xml:lang="en">We consider the NP-hard problem of finding a spanning tree with a maximum number of internal vertices. This problem is a generalization of the famous HAMILTONIAN PATH problem. Our dynamic-programming algorithms for general and degree-bounded graphs have running times of the form O<sup>*</sup>
(c<sup>n</sup>
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) when analyzed with respect to the number of vertices. We also show that its running time is 2.1364<sup>k</sup>
n<sup>O(1)</sup>
 when the goal is to find a spanning tree with at least k internal vertices. Both running time bounds are obtained via a Measure & Conquer analysis, the latter one being a novel use of this kind of analysis for parameterized algorithms.</div>
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Exact and Parameterized Algorithms for MAX INTERNAL SPANNING TREE

Exact and Parameterized Algorithms for MAX INTERNAL SPANNING TREE

Source :

Descripteurs français

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri