# Tight approximation algorithm for connectivity augmentation problems

Guy Kortsarz, Zeev Nutov

نتاج البحث: فصل من :كتاب / تقرير / مؤتمرمنشور من مؤتمرمراجعة النظراء

## ملخص

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).

اللغة الأصلية الإنجليزيّة Automata, Languages and Programming - 33rd International Colloquium, ICALP 2006, Proceedings Springer Verlag 443-452 10 3540359044, 9783540359043 https://doi.org/10.1007/11786986_39 نُشِر - 2006 33rd International Colloquium on Automata, Languages and Programming, ICALP 2006 - Venice, إيطالياالمدة: ١٠ يوليو ٢٠٠٦ → ١٤ يوليو ٢٠٠٦

### سلسلة المنشورات

الاسم Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 4051 LNCS 0302-9743 1611-3349

### !!Conference

!!Conference 33rd International Colloquium on Automata, Languages and Programming, ICALP 2006 إيطاليا Venice ١٠/٠٧/٠٦ → ١٤/٠٧/٠٦

## بصمة

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