Exact and Parameterized Algorithms for Max Internal Spanning Tree
Identifieur interne : 000C36 ( Main/Exploration ); précédent : 000C35; suivant : 000C37Exact and Parameterized Algorithms for Max Internal Spanning Tree
Auteurs : Henning Fernau [Allemagne] ; Serge Gaspers [France] ; Daniel Raible [Allemagne]Source :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2010.
Abstract
Abstract: We consider the $\mathcal{NP}$ -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 *(c n ) (c ≤ 3). 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(1.8669 n ) when analyzed with respect to the number of vertices. We also show that its running time is 2.1364 k n 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.
Url:
DOI: 10.1007/978-3-642-11409-0_9
Affiliations:
- Allemagne, France
- Languedoc-Roussillon, Occitanie (région administrative), Rhénanie-Palatinat
- Montpellier, Trèves (Allemagne)
- Université de Trèves
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Le document en format XML
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<front><div type="abstract" xml:lang="en">Abstract: We consider the $\mathcal{NP}$ -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 *(c n ) (c ≤ 3). 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(1.8669 n ) when analyzed with respect to the number of vertices. We also show that its running time is 2.1364 k n 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.</div>
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