The periodic balanced sorting network
Journal of the ACM (JACM)
Introduction to algorithms
ACM Computing Surveys (CSUR)
Journal of the ACM (JACM)
Coins, weights and contention in balancing networks
PODC '94 Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing
Contention in counting networks
PODC '94 Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing
Self-stabilizing systems in spite of distributed control
Communications of the ACM
Counting networks with arbitrary fan-out
Distributed Computing
Sorting networks and their applications
AFIPS '68 (Spring) Proceedings of the April 30--May 2, 1968, spring joint computer conference
Journal of Parallel and Distributed Computing - Special issue: 18th International parallel and distributed processing symposium
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A smoothing network is a distributed data structure thataccepts tokens on input wires and routes them to outputwires. It ensures that however imbalanced the traffic oninput wires, the numbers of tokens emitted on output wiresare approximately balanced.Prior work on smoothing networks always assumed thatsuch networks were properly initialized. In a real distributedsystem, however, network switches may be rebootedor replaced dynamically, and it may not be practical to determinethe correct initial state for the new switch. Prioranalyses do not work under these new assumptions.This paper makes the following contributions. First, weshow that some well-known 1-smoothing networks, knownas counting networks, when started in an arbitrary initialstate (perhaps chosen by an adversary), remain remarkablysmooth, degrading from 1-smooth to log(n)-smooth, wheren is the number of input/output wires.Second, we show that the same networks can be madeeventually 1-smooth by "piggy-backing" a small amount ofadditional information on messages when (and only when)trouble is detected.