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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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></front></TEI><affiliations><list><country><li>Allemagne</li><li>France</li></country><region><li>Languedoc-Roussillon</li><li>Occitanie (région administrative)</li><li>Rhénanie-Palatinat</li></region><settlement><li>Montpellier</li><li>Trèves (Allemagne)</li></settlement><orgName><li>Université de Trèves</li></orgName></list><tree><country name="Allemagne"><region name="Rhénanie-Palatinat"><name sortKey="Fernau, Henning" sort="Fernau, Henning" uniqKey="Fernau H" first="Henning" last="Fernau">Henning Fernau</name></region><name sortKey="Fernau, Henning" sort="Fernau, Henning" uniqKey="Fernau H" first="Henning" last="Fernau">Henning Fernau</name><name sortKey="Raible, Daniel" sort="Raible, Daniel" uniqKey="Raible D" first="Daniel" last="Raible">Daniel Raible</name><name sortKey="Raible, Daniel" sort="Raible, Daniel" uniqKey="Raible D" first="Daniel" last="Raible">Daniel Raible</name></country><country name="France"><region name="Occitanie (région administrative)"><name sortKey="Gaspers, Serge" sort="Gaspers, Serge" uniqKey="Gaspers S" first="Serge" last="Gaspers">Serge Gaspers</name></region><name sortKey="Gaspers, Serge" sort="Gaspers, Serge" uniqKey="Gaspers S" first="Serge" last="Gaspers">Serge Gaspers</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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