Exact and Parameterized Algorithms for Max Internal Spanning Tree (2009)
| Citations: | 2 - 2 self |
BibTeX
@MISC{Fernau09exactand,
author = {Henning Fernau and Serge Gaspers and Daniel Raible},
title = {Exact and Parameterized Algorithms for Max Internal Spanning Tree },
year = {2009}
}
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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 ∗ (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.
