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(u,v) : u, v ∈ V}. The goal is to find a weight assignment w = {w v : v ∈ V} of minimum total weight w(V) = v∈V w v, such that: for all u, v ∈ V, the activated graph G w = (V,E w ), where E w = {uv : f uv (w u ,w v)=1}, contains r(u,v) 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 [12], 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(κ logn) for κ-Out/In-connected Subgraph Activation and κ-Connected Subgraph Activation. For directed graphs this solves a question from [12] for κ = 1, while for the min-power case and κ arbitrary this solves an open question from [9]. For other versions on undirected graphs, our ratios match the best known ones for the Node-Weighted Survivable Network problem [8]. © 2012 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Nutov, Z. (2012). Survivable network activation problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7256 LNCS, pp. 594–605). https://doi.org/10.1007/978-3-642-29344-3_50
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