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<p><b>Abstract</b>—Uniformly random or Poisson distributions are widely accepted models for the location of the nodes in wireless sensor networks if nodes are deployed in large quantities and there is little control over where they are dropped. On the other hand, by placing nodes in regular topologies, we expect benefits both in coverage and efficiency of communication. We describe and analyze a basic localized algorithm and three modifications for topology control that provide a tradeoff between performance and deployment cost. The objective is to regularize the topology for improved energy efficiency. The basic algorithm produces quasiregular networks, which only use nodes as sentries and relays that are approximately evenly spaced, thereby emulating a regular grid topology. It is shown that quasiregular networks have a significant energy and lifetime advantage compared with purely random networks. We consider two specific types of quasiregular networks: the ones that are based on a Gaussian deviation about an ideal grid point (type A), and the ones that consist of a subset of nodes taken from a Poisson point process (type B). We show that the two types are equivalent for a certain density of the Poisson point process and, in particular, that in both cases the deviation from the ideal regular grid follows a Rayleigh distribution, whereas the distance between nearest neighbors is Ricean.</p>
Wireless sensor networks, wireless communications, network topology, network protocols, Poisson point processes, Rayleigh fading.

X. Liu and M. Haenggi, "Toward Quasiregular Sensor Networks: Topology Control Algorithms for Improved Energy Efficiency," in IEEE Transactions on Parallel & Distributed Systems, vol. 17, no. , pp. 975-986, 2006.
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