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 ...

• Type: Conference
• Year: 2009
• Where: APPROX
• Authors: Zeev Nutov
• Keywords: Algorithms, APPROX 2009, Connectivity Augmentation, Node Connectivity Augmentation, Rooted NCA