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Article Dans Une Revue Mathematical Programming Année : 2022

Flexible Graph Connectivity

Résumé

We introduce and study the problem Flexible Graph Connectivity, which in contrast to many classical connectivity problems features a non-uniform failure model. We distinguish between safe and unsafe resources and postulate that failures can only occur among the unsafe resources. Given an undirected edge-weighted graph and a set of unsafe edges, the task is to find a minimum-cost subgraph that remains connected after removing at most k unsafe edges. We give constant-factor approximation algorithms for this problem for k = 1 as well as for unit costs and k ≥ 1. Our approximation guarantees are close to the known best bounds for special cases, such as the 2-edge-connected spanning subgraph problem and the tree augmentation problem. Our algorithm and analysis combine various techniques including a weight-scaling algorithm, a charging argument that uses a variant of exchange bijections between spanning trees and a factor revealing min–max–min optimization problem.
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Dates et versions

hal-04215559 , version 1 (22-09-2023)

Identifiants

Citer

David Adjiashvili, Felix Hommelsheim, Moritz Mühlenthaler. Flexible Graph Connectivity. Mathematical Programming, 2022, 192 (1-2), pp.409-441. ⟨10.1007/s10107-021-01664-9⟩. ⟨hal-04215559⟩
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