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.Comment: 20 pages, 22 figure