Approximating the minmax subtree cover problem in a cactus

Authors:
Hiroshi Nagamochi;Taizo Kawada
Affiliations:
Kyoto University, Kyoto, Japan;Toyohashi University of Technology, Toyohashi, Japan
Venue:
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Year:
2004

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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 χ = {X1,X2,...,Xp} of V and a set of p subtrees T1,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 Ti and the weights of vertices in Xi In this paper, we propose an O(p2n) time (4– 4/(p + 1))-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.