TY - GEN

T1 - Tight approximation algorithm for connectivity augmentation problems

AU - Kortsarz, Guy

AU - Nutov, Zeev

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2006

Y1 - 2006

N2 - The S-connectivity λGS(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, E0), 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 λG0+FS(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(2log1-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(rmax · log n) for S = V, where rmax = maxu,vεV r(u, v).

AB - The S-connectivity λGS(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, E0), 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 λG0+FS(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(2log1-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(rmax · log n) for S = V, where rmax = maxu,vεV r(u, v).

UR - http://www.scopus.com/inward/record.url?scp=33746354966&partnerID=8YFLogxK

U2 - 10.1007/11786986_39

DO - 10.1007/11786986_39

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AN - SCOPUS:33746354966

SN - 3540359044

SN - 9783540359043

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 443

EP - 452

BT - Automata, Languages and Programming - 33rd International Colloquium, ICALP 2006, Proceedings

PB - Springer Verlag

T2 - 33rd International Colloquium on Automata, Languages and Programming, ICALP 2006

Y2 - 10 July 2006 through 14 July 2006

ER -