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  • Zeev Nutov
  • 2009 50th Annual IEEE Symposium on Foundations of…
  • 2009
We give approximation algorithms for the Survivable Network problem. The input consists of a graph <i>G</i> = (<i>V,E</i>) with edge/node-costs, a node subset <i>S</i> &#8838; <i>V</i>, and connectivity requirements {<i>r</i>(<i>s,t</i>):<i>s,t</i> &#8712; <i>T</i> &#8838; <i>V</i>}. The goal is to find a minimum cost subgraph <i>H</i> of <i>G</i> that for(More)
We survey approximation algorithms and hardness results for versions of the Generalized Steiner Network (GSN) problem in which we seek to find a low cost subgraph (where the cost of a subgraph is the sum of the costs of its edges) that satisfies prescribed connectivity requirements. These problems include the following well known problems: min-cost k-flow,(More)
The (undirected) Steiner Network problem is as follows: given a graphG = (V, E) with edge/node-weights and edge-connectivity requirements {r(u, v) : u, v ∈ U ⊆ V }, find a minimumweight subgraph H of G containing U so that the uv-edge-connectivity in H is at least r(u, v) for all u, v ∈ U . The seminal paper of Jain [Combinatorica, 21 (2001), pp. 39–60],(More)
In the Survivable Network Design Problem (SNDP) one seeks to find a minimum cost subgraph that satisfies prescribed node-connectivity requirements. We give a novel approximation ratio preserving reduction from Directed SNDP to Undirected SNDP. Our reduction extends and widely generalizes as well as significantly simplifies the main results of [9]. Using it,(More)
Let <i>G</i> = (<i>V, E</i>) be a graph and let <i>S</i> &#8838; <i>V.</i> The <i>S-connectivity</i> &#955;<i>s</i>(<i>u, v; G</i>) of <i>u</i> and <i>v</i> in <i>G</i> is the maximum number of <i>uv</i>-paths that no two of them have an edge or a node in <i>S</i> - {<i>u, v</i>} in common. The corresponding <i>Connectivity Augmentation Problem (CAP)</i>(More)
The (undirected) Rooted Survivable Network Design (Rooted SND) problem is: given a complete graph on node set V with edge-costs, a root s ∈ V , and (node-)connectivity requirements {r(t) : t ∈ T ⊆ V }, find a minimum cost subgraph G that contains r(t) internally-disjoint st-paths for all t ∈ T . For large values of k = maxt∈T r(t) Rooted SND is at least as(More)