A constant-factor approximation algorithm for the k-MST problem

Abstract

Given an undirected graph with nonnegative edge costs and an integer k, the k-MST problem is that of finding a tree of minimum cost on k nodes. This problem is known to be NP-hard. We present a simple approximation algorithm that finds a solution whose cost is less than 17 times the cost of the optimum. This improves upon previous performance ratios for this problem -O(√k) due to Ravi et al., O(log2k) due to Awerbuch et al., and the previous best bound of O(logk) due to Rajagopalan and Vazirani. Given any 0