Approximating the minmax subtree cover problem in a cactus

Abstract

Let G -(V, E) be a connected graph such that edges and vertices are weighted by nonnegative reals. Let p be a positive integer. The minmax subtree cover problem (MSC) asks to find a partition X = {X1,X 2,...,Xp} of V and a set of p subtrees T 1,T2,... ,Tp, each Ti containing Xi so as to minimize the maximum cost of the subtrees, where the cost of Ti is defined to be the sum of the weights of edges in T i and the weights of vertices in Xi. In this paper, we propose an O(p2n) time (4 -4/(p+l))-approximation algorithm for the MSC when G is a cactus. This is the first constant factor approximation algorithm for the MSC on a class of non-tree graphs. © Springer-Verlag 2004.