Faster radio broadcasting in planar graphs

We study the communication primitive of broadcasting (one-to-all communication) in known topology radio networks, i.e., where for each primitive the schedule of transmissions is precomputed based on full knowledge about the size and the topology of the network. We show that radio broadcasting can be completed in D+O(logn) time units in planar graphs of size n, diameter D, which improves the currently best known D+O(log
³
n) time schedule proposed by Elkin and Kortsarz in (2005) [SODA'05], and 3D time schedule due to Gasieniec, Peleg and Xin in (2005) [PODC'05]