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<p><b>Abstract</b>—We propose a novel localized topology-control algorithm for each wireless node to locally select communication neighbors and adjust its transmission power accordingly such that all nodes together self-form a topology that is energy efficient simultaneously for both unicast and broadcast communications. We theoretically prove that the proposed topology is <it>planar</it>, which meets the requirement of certain localized routing methods to guarantee packet delivery; it is power-efficient for unicast—the energy needed to connect any pair of nodes is within a small constant factor of the minimum; it is also asymptotically optimum for broadcast—the energy consumption for broadcasting data on top of it is asymptotically the best among all structures constructed using only local information; it has a constant bounded logical degree, which will potentially save the cost of updating routing tables if used. We further prove that the expected average physical degree of all nodes is a small constant. To the best of our knowledge, this is the <it>first</it> localized topology-control strategy for all nodes to maintain a structure with all these desirable properties. Previously, only a centralized algorithm was reported in [CHECK END OF SENTENCE]. Moreover, by assuming that the node ID and its position can be represented in <tmath>O(\log n)</tmath> bits for a wireless network of <tmath>n</tmath> nodes, the total number of messages by our methods is in the range of <tmath>[5n,13n]</tmath>, where each message is <tmath>O(\log n)</tmath> bits. Our theoretical results are corroborated in the simulations.</p>
Graph theory, localized communication, wireless ad hoc networks, topology control, power efficient, low weight, low interference, unicast, broadcast.
WeiZhao Wang, Xiang-Yang Li, Ophir Frieder, Wen-Zhan Song, "Localized Topology Control for Unicast and Broadcast in Wireless Ad Hoc Networks", IEEE Transactions on Parallel & Distributed Systems, vol. 17, no. , pp. 321-334, April 2006, doi:10.1109/TPDS.2006.53
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