Abstract
Given an undirected graph G(V,E) with terminal set T ⊆ V the problem of packing element-disjoint Steiner trees is to find the maximum number of Steiner trees that are disjoint on the nonterminal nodes and on the edges. The problem is known to be NP-hard to approximate within a factor of Ω(logn), where n denotes |V|. We present a randomized O(logn)-approximation algorithm for this problem, thus matching the hardness lower bound. Moreover, we show a tight upper bound of O(logn) on the integrality ratio of a natural linear programming relaxation.
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Cheriyan, J., Salavatipour, M.R. (2005). Packing Element-Disjoint Steiner Trees. In: Chekuri, C., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2005 2005. Lecture Notes in Computer Science, vol 3624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538462_5
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DOI: https://doi.org/10.1007/11538462_5
Publisher Name: Springer, Berlin, Heidelberg
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