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Given a set of positions for wireless nodes, the interference minimization problem is to assign a transmission radius (equivalently, a power level) to each node such that the resulting communication graph is connected, while minimizing the maximum interference. We consider the model introduced by von Rickenbach et al. (2005), in which each transmission range is represented by a ball and edges in the communication graph are symmetric. The problem is NP-complete in two dimensions (Buchin 2008) and no polynomial-time approximation algorithm is known. In this paper we show how to solve the problem efficiently in settings typical for wireless ad hoc networks. We show that if node positions are represented by a set P of n points selected uniformly and independently at random over a d-dimensional rectangular region, for any fixed d, then the topology given by the closure of the Euclidean minimum spanning tree of P has maximum interference O(logn) with high probability. We extend this 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 the expected maximum interference. Finally, we analyze an empirical evaluation of our algorithm by simulation.

Bounding Interference in Wireless Ad Hoc Networks with Nodes in Random Position