A Fault Tolerant Approximate BFS Structures

A fault-tolerant structure for a network is required to continue functioning following the failure of some of the network’s edges or vertices. This paper addresses the problem of designing a fault-tolerant (α, β) approximate BFS structure (or FT-ABFS structure for short), namely, a subgraph H of the network G such that subsequent to the failure of some subset F of edges or vertices, the surviving part of H (namely, H \ F ) still contains an approximate BFS spanning tree for (the surviving part of) G, satisfying dist(s, v,H \ F ) ≤ α · dist(s, v,G \ F ) + β for every v ∈ V .