Broadcasting in UDG Radio Networks with Missing and Inaccurate Information [chapter]

Emanuele G. Fusco, Andrzej Pelc
<i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
when optimal time is O(D). Nevertheless, under our very weak scenario, we construct a broadcasting algorithm that maintains optimal time O min D + g 2 , D log g for all networks with at least 2 nodes, of diameter D and granularity g (previously obtained with exact positions and known density), if each node perceives its position with error margin ε = αd, for any (unknown) constant α < 1/2. Rather surprisingly, the minimum time of an algorithm working correctly for all networks, and hence
more &raquo; ... g if the source is alone, turns out to be Θ (D + g 2 ). Thus, the mere stopping requirement for the special case of the lonely source causes an exponential increase in broadcasting time, for networks of any density and any small diameter. Finally, if ε ≥ d/2, then broadcasting is impossible.
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