We consider several problems relating to stronglyconnected directed networks of identical finite-state processors that work synchronously in discrete time steps. The conceptually simplest of these problems 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 macrosynchronization 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[6] that these two problems in particular are asymptotically timeequivalent up to a constant factor. This result leads immediately to the inclusion of several other related problems into this new asymptotic time-class.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.