Minmax subtree cover problem on cacti

Authors:
Hiroshi Nagamochi;Taizo Kawada
Affiliations:
Kyoto University, Yoshida Honmachi, Sakyo, Kyoto 606-8501, Japan;Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Aichi 441-8580, 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,T) of a partition X={X"1,X"2,...,X"p} of V and a set T of p subtrees T"1,T"2,...,T"p, each T"i containing X"i so as to minimize the maximum cost of the subtrees, where the cost of T"i is defined to be the sum of the weights of edges in T"i and the weights of vertices in X"i. In this paper, we propose an O(p^2n) time (4-4/(p+1))-approximation algorithm for the MSC when G is a cactus.