Tight approximation algorithm for connectivity augmentation problems

Guy Kortsarz, Zeev Nutov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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).

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 33rd International Colloquium, ICALP 2006, Proceedings
PublisherSpringer Verlag
Number of pages10
ISBN (Print)3540359044, 9783540359043
StatePublished - 2006
Event33rd International Colloquium on Automata, Languages and Programming, ICALP 2006 - Venice, Italy
Duration: 10 Jul 200614 Jul 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4051 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference33rd International Colloquium on Automata, Languages and Programming, ICALP 2006


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