## Abstract

In the Survivable Networks Activation problem we are given a graph G=(V,E), S⊂V, a family {f_{uv}(x_{u},x_{v}):uv∈E} of monotone non-decreasing activating functions from R+2 to {0,1} each, and connectivity requirements {r(uv):uv∈R} over a set R of requirement edges on V. The goal is to find a weight assignment w={w_{v}:v∈V} of minimum total weight w(V)=Σ_{v∈V}w_{v}, such that in the activated graph G_{w}=(V, E_{w}), where E_{w}={uv: f_{uv}(w_{u},w_{v})=1}, the following holds: for each uv∈R, the activated graph ^{Gw} contains r(uv) pairwise edge-disjoint uv-paths such that no two of them have a node in S\-{u,v} in common. This problem was suggested recently by Panigrahi (2011) [19], generalizing the Node-Weighted Survivable Network and the Minimum-Power Survivable Network problems, as well as several other problems with motivation in wireless networks. We give new approximation algorithms for this problem. For undirected/directed graphs, our ratios are O(klogn) for k-Out/In-connected Subgraph Activation and k-Connected Subgraph Activation. For directed graphs this solves a question from Panigrahi (2011) [19] for k=1, while for the min-power case and k arbitrary this solves a question from Nutov (2010) [16]. For other versions on undirected graphs, our ratios match the best known ones for the Node-Weighted Survivable Network problem (Nutov, 2009 [14]).

Original language | English |
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Pages (from-to) | 105-115 |

Number of pages | 11 |

Journal | Theoretical Computer Science |

Volume | 514 |

DOIs | |

State | Published - 25 Nov 2013 |

## Keywords

- Approximation algorithms
- Graph-connectivity
- Network design
- Wireless networks