Polynomial time 2-approximation algorithms for the minmax subtree cover problem

Abstract

Let T be a tree such that edges are weighted by nonnegative reals, and p be a positive integer. The minmax subtree cover problem asks to find a set of p subtrees such that the union of the subtrees covers all vertices in T, where the objective is to minimize the maximum weight of the subtrees. Given a root r in T, the minmax rooted-subtree cover problem asks to find a set of p subtrees such that each subtree contains the root r and the union of the subtrees covers all vertices in T, where the objective is to minimize the maximum weight of the subtrees. In this paper, we propose an O(p2n) time (2 - 2/p+1)-approximation algorithm to the first problem, and an O(n log log1+ε/2 3) time (2 + ε)-approximation algorithm to the second problem, where ε > 0 is a prescribed constant. © Springer-Verlag Berlin Heidelberg 2003.