A 43-approximation algorithm for the Maximum Internal Spanning Tree Problem

摘要

In this paper, we study the Maximum Internal Spanning Tree Problem (MIST). Given an undirected simple graph G, the task for the Maximum Internal Spanning Tree problem is to find a spanning tree of G with maximum number of internal vertices. We present an approximation algorithm with performance ratio 43, which improves upon the best known performance ratio 32. Our algorithm benefits from a new observation for bounding the number of internal vertices of a spanning tree. We can also give an example to show that the performance ratio 43 is actually tight for this algorithm. Finally, we show that MIST is Max-SNP-hard.