Survivable network activation problems

• Authors: Zeev Nutov
• Venue: LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
• Year: 2012

In the Survivable Networks Activation problem we are given a graph G=(V,E), S⊆V, a family {fuv(xu,xv):uv∈E} of monotone non-decreasing activating functions from ℝ2+ to {0,1} each, and connectivity requirements {r(u,v):u,v∈V}. The goal is to find a weight assignmentw={wv:v∈V} of minimum total weight w(V)=∑v∈Vwv, such that: for all u,v∈V, the activated graphGw=(V,Ew), where Ew={uv:fuv(wu,wv)=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(k logn) for k-Out/In-connected Subgraph Activation and k-Connected Subgraph Activation. For directed graphs this solves a question from [12] for k=1, while for the min-power case and k 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].