Fault tolerant additive and [formula omitted]-spanners

Abstract

Graph spanners are sparse subgraphs that preserve the distances of the original graph up to some approximation ratio (the spanner's stretch). A number of algorithms are known for constructing sparse spanners with small multiplicative or additive stretch. Recently, algorithms were introduced for constructing fault-tolerant multiplicative spanners of general graphs. This paper addresses the analogous problem of constructing fault tolerant additive and (μ,α)-spanners for general graphs, and presents a number of (deterministic and randomized) construction algorithms for such spanners.