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Average size of unstretched RemoteSpanners
, 2008
"... Motivated by the optimization of link state routing in ad hoc networks, and the concept of multipoint relays, we introduce the notion of remotespanner. Given an unweighted graph G, a remote spanner is a set of links H such that for any pair of nodes (u, v) there exists a shortest path in G for whic ..."
Abstract

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Motivated by the optimization of link state routing in ad hoc networks, and the concept of multipoint relays, we introduce the notion of remotespanner. Given an unweighted graph G, a remote spanner is a set of links H such that for any pair of nodes (u, v) there exists a shortest path in G for which all links in the path that are not adjacent to u belong to H. The remote spanner is a kind of minimal topology information beyond its neighborhood that any node would need in order to compute its shortest paths in a distributed way. This can be extended to kconnected graphs by considering minimum length sum over k disjoint paths as distance. In this paper, we give distributed algorithms for computing remotespanners in order to obtain sparse remotespanners with various properties. We provide a polynomial distributed algorithm that computes a kconnecting unstretched remotespanner whose number of edges is at a factor 2(1 + log ∆) from optimal where ∆ is the maximum degree of a node. Interestingly, its expected compression ratio in number of edges is O ( k n log n) in ErdösRényi graph model and O( ( k 2 n) 3) in the unit disk graph model with a uniform Poisson distribution of nodes. 1