Minmax subtree cover problem on cacti

Authors:
Hiroshi Nagamochi;Taizo Kawada
Affiliations:
Kyoto University, Yoshida Honmachi, Sakyo, Kyoto, Japan;Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Aichi, Japan
Venue:
Discrete Applied Mathematics
Year:
2006

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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 pair (X,F) of a partition X = {X1,X2,...,Xp} of V and a set F 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.