The Wake Up and Report Problem is Time-Equivalent to the Firing Squad Synchronization Problem
Abstract
We consider several problems relating to strongly-connected directed networks of identical finite-state processors that work synchronously in discrete time steps. The conceptually simplest of these is the Wake Up and Report Problem; this is the problem of having a unique "root" processor send a signal to all other processors in the network and then enter a special "done" state only when all other processors have received the signal. The most difficult of the problems we consider is the classic Firing Squad Synchronization Problem; this is the much-studied problem of achieving macro-synchronization in a network given micro-synchronization. We show via a complex algorithmic application of the "snake" data structure first introduced in Even, Litman, and Winkler [ELW], that these two problems are asymptotically time-equivalent up to a constant factor. This result leads immediately to the inclusion of several other related problems into this new asymptotic time-class.
Keywords
Cite
@article{arxiv.cs/0310003,
title = {The Wake Up and Report Problem is Time-Equivalent to the Firing Squad Synchronization Problem},
author = {Darin Goldstein and Nick Meyer},
journal= {arXiv preprint arXiv:cs/0310003},
year = {2007}
}
Comments
13 pages, 4 figures, in Symposium on Discrete Algorithms, (SODA) pp. 578-587, January 6-8, 2002 (journal version to appear in the Journal of Distributed Computing)