An $\Omega(D\log (N/D))$ Lower Bound for Broadcast in Radio Networks
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We show new lower bounds for collision-free transmissions in Radio Networks. Our main result is a tight lower bound of Ω(log n log (1/ε)) on the time required by a uniform randomized protocol to achieve a clear transmission with success probability 1–ε in a one-hop setting. This result is extended to non-uniform protocols as well. A new lower bound is proved for the important multi-hop setting of nodes distributed as a connected Random Geometric Graph. Our main result is tight for a variety of problems.