Improved Approximations for Relative Survivable Network Design

Michael Dinitz, Ama Koranteng, Guy Kortsarz, Zeev Nutov

Abstract: One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands (e.g. the Minimum k-Edge-Connected Spanning Subgraph problem), as well as nonuniform demands (e.g. the Survivable Network Design problem (SND)). In a recent paper [Dinitz, Koranteng, Kortsarz APPROX ’22], the authors observed that a weakness of these formulations is that we cannot consider fault-tolerance in graphs that have small cuts but where some large fault sets can still be accommodated. To remedy this, they introduced new variants of these problems under the notion relative fault-tolerance. Informally, this requires not that two nodes are connected if there are a bounded number of faults (as in the classical setting), but that they are connected if there are a bounded number of faults and the nodes are connected in the underlying graph post-faults.