Synchronization Landscapes in Small-World-Connected Computer Networks

TL;DR

This study investigates how small-world network structures influence synchronization in distributed computing, showing that adding random links reduces fluctuations and promotes uniform progress among processors.

Contribution

It demonstrates that small-world networks suppress synchronization fluctuations and achieve stable, near-uniform processor progress without global control, unlike regular networks.

Findings

Regular networks exhibit kinetic roughening with diverging fluctuations.

Adding random links leads to finite synchronization width.

Small-world networks enable near-uniform, stable processor progress.

Abstract

Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two-dimensions. We find that the synchronization landscape (corresponding to the progress of the individual processors) exhibits Kardar-Parisi-Zhang-like kinetic roughening on regular networks with short-range communication links. Although the processors, on average, progress at a nonzero rate, their spread (the width of the synchronization landscape) diverges with the number of nodes (desynchronized state) hindering efficient data management. When random communication links are added on top of the one and two-dimensional regular networks (resulting in a small-world network), large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system-size limit (synchronized state). In the resulting synchronization scheme, the processors make close-to-uniform progress with a nonzero rate without global intervention. We obtain our results by ``simulating the simulations", based on the exact algorithmic rules, supported by coarse-grained arguments.