 
Summary: A 2 + # approximation algorithm for the kMST problem
Sanjeev Arora #
Princeton University
George Karakostas +
Princeton University
Abstract
For any # > 0 we give a (2+#)approximation al
gorithm for the problem of finding a minimum tree
spanning any k vertices in a graph (kMST), improv
ing a 3approximation algorithm by Garg [5]. As
in [5] the algorithm extends to a (2+#)approximation
algorithm for the minimum tour that visits any k ver
tices, provided the edge costs satisfy the triangle in
equality.
1 Introduction
Given an undirected graph G = (V, E) with non
negative edge costs and an integer k, the kMST
problem is that of finding a tree of minimum cost that
spans exactly k vertices of G; we call such a tree a
ktree. The problem is known to be NPcomplete.
