The S-connectivity λ G S (u, v) of (u, v) in a graph G is the maximum number of uv-paths that no two of them have an odgo or a node in S - {u, v} in common. The corresponding Connectivity Augmentation (CA) problem is: given a graph Go = (V, E 0), S ⊆ V, and requirements r(u,v) on V × V, find a minimum size set F of new edges (any edge is allowed) so that λ G0+F S (u, v) ≥ r(u, v) for all u, v ε V. Extensively studied particular cases are the edge-CA (when S = Ø) and the node-CA (when S = V). A. Frank gave a polynomial algorithm for undirected edge-CA and observed that the directed case even with r(u, v) ε {0,1} is at least as hard as the Set-Cover problem. Both directed and undirected node-CA have approximation threshold Ω(2 log1-E n). We give an approximation algorithm that matches these approximation thresholds. For both directed and undirected CA with arbitrary requirements our approximation ratio is: O(log n) for S ≠ V arbitrary, and O(r max · log n) for S = V, where r max = max u,vεV r(u, v). © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Kortsarz, G., & Nutov, Z. (2006). Tight approximation algorithm for connectivity augmentation problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4051 LNCS, pp. 443–452). Springer Verlag. https://doi.org/10.1007/11786986_39
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