Extensions of the (p,q)-Flexible-Graph-Connectivity model

11/17/2022

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by   Ishan Bansal, et al.

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We present approximation algorithms for network design problems in some models related to the (p,q)-FGC model. Adjiashvili, Hommelsheim and Mühlenthaler introduced the model of Flexible Graph Connectivity that we denote by FGC. Boyd, Cheriyan, Haddadan and Ibrahimpur introduced a generalization of FGC. Let p≥ 1 and q≥ 0 be integers. In an instance of the (p,q)-Flexible Graph Connectivity problem, denoted (p,q)-FGC, we have an undirected connected graph G = (V,E), a partition of E into a set of safe edges and a set of unsafe edges, and nonnegative costs c∈ℝ_≥0^E on the edges. A subset F ⊆ E of edges is feasible for the (p,q)-FGC problem if for any set of unsafe edges, F', with |F'|≤ q, the subgraph (V, F ∖ F') is p-edge connected. The algorithmic goal is to find a feasible edge-set F that minimizes c(F) = ∑_e ∈ F c_e.