Distributed Proximity Maintenance in Ad Hoc Mobile Networks

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We present an efficient distributed data structure, called the d-Spanner, for maintaining proximity information among communicating mobile nodes. The d-Spanner is a kinetic sparse graph spanner on the nodes that allows each node to quickly determine which other nodes are within a given distance of itself, to estimate an approximate nearest neighbor, and to perform a variety of other proximity related tasks. A lightweight and fully distributed implementation is possible, in that maintenance of the proximity information only requires each node to exchange a modest number of messages with a small number of mostly neighboring nodes. The structure is based on distance information between communicating nodes that can be derived using ranging or localization methods and requires no additional shared infrastructure other than an underlying communication network. Its modest requirements make it scalable to networks with large numbers of nodes.