Spanner of an undirected graph G = (V, E) is a subgraph which is sparse and yet preserves all-pairs distances approximately. More formally, a spanner with stretch t ∈ N is a subgraph (V, ES), ES ⊆ E such that the distance between any two vertices in the subgraph is at most t times their distance in G. Though G is trivially a t-spanner of itself, the research as well as applications of spanners invariably deal with a t-spanner which has as small number of edges as possible.We present fully dynamic algorithms for maintaining spanners in centralized as well as synchronized distributed environments. These algorithms are designed for undirected unweighted graphs and use randomization in a crucial manner.Our algorithms significantly improve the existing fully dynamic algorithms for graph spanners. The expected size (number of edges) of a t-spanner maintained at each stage by our algorithms matches, up to a poly-logarithmic factor, the worst case optimal size of a t-spanner. The expected amortized time (or messages communicated in distributed environment) to process a single insertion/deletion of an edge by our algorithms is close to optimal. * The results of the preliminary version of this article appeared in ESA 2006 and SODA 2008
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.