Exact Exponential Time Algorithms for Max Internal Spanning Tree
Abstract
We consider the NPhard 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 dynamicprogramming algorithms for general and degreebounded 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2008
 arXiv:
 arXiv:0811.1875
 Bibcode:
 2008arXiv0811.1875F
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Discrete Mathematics