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(p 2 n) time \((2 - \frac{2}{p+1})\)-approximation algorithm to the first problem, and an \(O(n{\rm log log_{1+\frac{\epsilon}{2}}3})\) time (2+ε)-approximation algorithm to the second problem, where ε> 0 is a prescribed constant.
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Nagamochi, H., Okada, K. (2003). Polynomial Time 2-Approximation Algorithms for the Minmax Subtree Cover Problem. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_16
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DOI: https://doi.org/10.1007/978-3-540-24587-2_16
Publisher Name: Springer, Berlin, Heidelberg
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