Approximating Node-Connectivity Augmentation Problems

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Approximating Node-Connectivity Augmentation Problems
The (undirected) Node Connectivity Augmentation (NCA) problem is: given a graph J = (V, EJ ) and connectivity requirements {r(u, v) : u, v ∈ V }, find a minimum size set I of new edges (any edge is allowed) so that J + I contains r(u, v) internally disjoint uv-paths, for all u, v ∈ V . In the Rooted NCA there is s ∈ V so that r(u, v) > 0 implies u = s or v = s. For large values of k = maxu,v∈V r(u, v), NCA is at least as hard to approximate as LabelCover and thus it is unlikely to admit a polylogarithmic approximation. Rooted NCA is at least as hard to approximate as Hitting-Set. The previously best approximation ratios for the problem were O(k ln n) for NCA and O(ln n) for Rooted NCA. In [Approximating connectivity augmentation problems, SODA 2005] the author posed the following open question: Does there exists a function ρ(k) so that NCA admits a ρ(k)-approximation algorithm? In this paper we answer this question, by giving an approximation algorithm with ratios O(k(1 ...
Zeev Nutov
Added 25 May 2010
Updated 25 May 2010
Type Conference
Year 2009
Authors Zeev Nutov
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