We consider a wireless network composed of a set of n wireless nodes distributed in a two dimensional plane. The signal sent by a node can be received by all nodes within its transmission region, which is a unit disk centered at this node. The nodes together define a unit disk graph (UDG) with edge uv iff ∥uv∥ ≤ 1. We present the first localized method to construct a bounded degree planar connected structure for UDG whose total edge length is within a constant factor of the minimum spanning tree. The total communication cost of our method is O(n), and every node only uses its two-hop information to construct such structure. We show that some two-hop information is necessary to construct any low-weighted structure. We also study the application of this structure in efficient broadcasting in wireless ad hoc networks. We prove that this structure uses only O(1/n) of the total energy of the previously best-known light weighted structure RNG. © Springer-Verlag Berlin Heidelberg 2003.
CITATION STYLE
Li, X. Y. (2003). Approximate MST for UDG locally. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2697, 364–373. https://doi.org/10.1007/3-540-45071-8_37
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