On the complexity of the “most general” firing squad synchronization problem

Authors:
Darin Goldstein;Kojiro Kobayashi
Affiliations:
Department of Computer Engineering and Computer Science, California State University, Long Beach;Department of Information Systems Science, Faculty of Engineering, Soka University
Venue:
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Year:
2006

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Abstract

We show that if a minimal-time solution exists for a fundamental distributed computation primitive, synchronizing a general directed network of finite-state processors, then there must exist an extraordinarily fast $O(ED log_2 D (log_2 n)^2)$ algorithm in the RAM model of computation for exactly determining the diameter of a general directed graph. The proof is constructive. This result interconnects two very distinct areas of computer science: distributed protocols on networks of intercommunicating finite-state machines and standard algorithms on the usual RAM model of computation.