A Faster Distributed Radio Broadcast Primitive: Extended Abstract

We present a faster distributed broadcasting primitive for the classical radio network model. The most basic distributed radio network broadcasting primitive - called Decay - dates back to a PODC'87 result of Bar-Yehuda, Goldreich, and Itai. In any radio network with some informed source nodes, running Decay for O(d log n + log2 n) rounds informs all nodes at most d hops away from a source with high probability. Since 1987 this primitive has been the most important building block for implementing many other functionalities in radio networks. The only improvements to this decades-old algorithm are slight variations due to [Czumaj, Rytter; FOCS'03] and [Kowalski and Pelc, PODC'03] which achieve the same functionality in O(d log n/d} + log2 n) rounds. To obtain a speedup from this, d and thus also the network diameter need to be near linear, i.e., larger than n1--ε. Our new distributed primitive spreads messages for d hops in O(d log n log log log d + logO(1) n) rounds with high probability. This improves over Decay for any super-polylogarithmic d = logω(1) n and achieves near-optimal O(d log log n) running time for d = nε. This also makes progress on an open question of Peleg.

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