Abstract
We consider the Tree Augmentation problem: given a graph G = (V,E) with edge-costs and a tree T on V disjoint to E, find a minimum-cost edge-subset F ⊆ E such that T ∪ F is 2-edge-connected. Tree Augmentation is equivalent to the problem of finding a minimum-cost edge-cover F ⊆ E of a laminar set-family. The best known approximation ratio for Tree Augmentation is 2, even for trees of radius 2. As laminar families play an important role in network design problems, obtaining a better ratio is a major open problem in network design. We give a (1 + ln 2)-approximation algorithm for trees of constant radius. Our algorithm is based on a new decomposition of problem solutions, which may be of independent interest.
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Cohen, N., Nutov, Z. (2011). A (1 + ln 2)-Approximation Algorithm for Minimum-Cost 2-Edge-Connectivity Augmentation of Trees with Constant Radius. In: Goldberg, L.A., Jansen, K., Ravi, R., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2011 2011. Lecture Notes in Computer Science, vol 6845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22935-0_13
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DOI: https://doi.org/10.1007/978-3-642-22935-0_13
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