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Bounding Interference in Wireless Ad Hoc Networks with Nodes in Random Position
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 2015
"... Given a set of positions for wireless nodes, the interference minimization problem is to assign a transmission radius (i.e., a power level) to each node such that the resulting communication graph is connected, while minimizing the maximum (respectively, average) interference. We consider the model ..."
Abstract

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Given a set of positions for wireless nodes, the interference minimization problem is to assign a transmission radius (i.e., a power level) to each node such that the resulting communication graph is connected, while minimizing the maximum (respectively, average) interference. We consider the model introduced by von Rickenbach et al. (2005), in which each wireless node is represented by a point in Euclidean space on which is centred a transmission range represented by a ball, and edges in the corresponding graph are symmetric. The problem is NPcomplete in two or more dimensions (Buchin 2008) and no polynomialtime approximation algorithm is known. We show how to solve the problem efficiently in settings typical for wireless ad hoc networks. If nodes are represented by a set P of n points selected uniformly and independently at random over a ddimensional rectangular region, then the topology given by the closure of the Euclidean minimum spanning tree of P has O(logn) maximum interference with high probability and O(1) expected interference. We extend the first bound to a general class of communication graphs over a broad set of probability distributions. We present a local algorithm that constructs a graph from this class; this is the first local algorithm to provide an upper bound on expected maximum interference. Finally, we disprove a conjecture of Devroye and Morin (2012) relating the maximum interference of the Euclidean minimum spanning tree to the optimal maximum interference attainable.