A (1 + ln 2)-Approximation Algorithm for Minimum-Cost 2-Edge-Connectivity Augmentation of Trees with Constant Radius [chapter]

Nachshon Cohen, Zeev Nutov
2011 Lecture Notes in Computer Science  
We consider the Tree Augmentation problem: given a graph = ( , ) with edge-costs and a tree on disjoint to , find a minimum-cost edge-subset ⊆ such that ∪ is 2-edge-connected. Tree Augmentation is equivalent to the problem of finding a minimumcost edge-cover ⊆ 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
more » ... 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.
doi:10.1007/978-3-642-22935-0_13 fatcat:2uejkjkgsbhqxklydgahc66cla