Summary: A 2.5 Factor Approximation Algorithm for the k-MST
The k-MST problem requires finding that subset of at least k vertices of a given
graph whose Minimum Spanning Tree has least weight amongst all subsets of at
least k vertices. There has been much work on this problem recently, culminating
in an approximation algorithm by Garg , which finds a subset of k vertices whose
MST has weight at most 3 times the optimal. Garg also argued that a factor of 3
cannot be improved unless lower bounds different from his are used. This argument
applies only to the rooted case of the problem. When no root vertex is specified,
we show how to use a pruning technique on top of Garg's algorithm to achieve
an approximation factor of 2.5. Note that Garg's algorithm is based upon the
Goemans-Williamson  clustering method, using which it seems hard to obtain
any approximation factor better than 2.
Key words: Approximation algorithms, k-MST problem.
The k-MST problem has received much attention in recent years. The first constant fac-
tor approximation algorithm for this problem on general graphs with non-negative edge