Exact Exponential Time Algorithms for Max Internal Spanning Tree
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 analyses for parameterized algorithms.
Cite
@article{arxiv.0811.1875,
title = {Exact Exponential Time Algorithms for Max Internal Spanning Tree},
author = {Henning Fernau and Serge Gaspers and Daniel Raible},
journal= {arXiv preprint arXiv:0811.1875},
year = {2009}
}