Fast deterministic distributed algorithms for sparse spanners

Abstract: This paper concerns the efficient construction of sparse and low stretch spanners for unweighted arbitrary graphs with nodes. All previous deterministic distributed algorithms, for constant stretch spanners of edges, have a running time for some constant depending on the stretch. Our deterministic distributed algorithms construct constant stretch spanners of edges in time for any constant . More precisely, in Linial’s free model a.k.a model, we construct in time, for every graph, a -spanner of edges, i.e., a spanning subgraph in which the distance is at most 3 times the distance of the original graph plus 2. The result is extended to -spanners with edges for every integer parameter , where . If the minimum degree of the graph is , then, in the same time complexity, a -spanner with edges can be constructed. [Copyright &y& Elsevier]