An improved algorithm for radio broadcast


We show that for every radio network <i>G</i> &equals; (<i>V</i>, <i>E</i>) and source <i>s</i> &#8712; <i>V</i>, there exists a radio broadcast schedule for <i>G</i> of length <i>Rad</i>(<i>G</i>, <i>s</i>) &plus; <i>O</i>(&sqrt;<i>Rad</i>(<i>G</i>, <i>s</i>) &#7777;log<sup>2</sup> <i>n</i>) &equals; <i>O</i>(<i>Rad</i>(<i>G</i>, <i>s</i>) &plus; log<sup>4</sup> <i>n</i>), where <i>Rad</i>(<i>G</i>, <i>s</i>) is the radius of the radio network <i>G</i> with respect to the source <i>s</i>. This result improves the previously best-known upper bound of <i>O</i>(<i>Rad</i>(<i>G</i>, <i>s</i>) &plus; log<sup>5</sup> <i>n</i>) due to Gaber and Mansour [1995]. For graphs with small genus, particularly for <i>planar</i> graphs, we provide an even better upper bound of <i>Rad</i>(<i>G</i>, <i>S</i>) &plus; <i>O</i>(&sqrt;<i>Rad</i>(<i>G</i>,<i>s</i>) &#7777; log <i>n</i> &plus; log<sup>3</sup> <i>n</i>) &equals; <i>O</i>(<i>Rad</i>(<i>G</i>, <i>s</i>) &plus; log<sup>3</sup> <i>n</i>).

DOI: 10.1145/1186810.1186818

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@article{Elkin2007AnIA, title={An improved algorithm for radio broadcast}, author={Michael Elkin and Guy Kortsarz}, journal={ACM Trans. Algorithms}, year={2007}, volume={3}, pages={8:1-8:21} }