Synchronization landscapes in small-world-connected computer networks

H. Guclu, G. Korniss, M. A. Novotny, Z. Toroczkai, and Z. Rácz

Phys. Rev. E 73, 066115 – Published 13 June 2006

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.

15 More

Received 26 December 2005

DOI:https://doi.org/10.1103/PhysRevE.73.066115

Authors & Affiliations

H. Guclu^* and G. Korniss

Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York, 12180-3590 USA

M. A. Novotny

Department of Physics and Astronomy, and Center for Computational Sciences, Mississippi State University, P. O. Box 5167, Mississippi State, Mississippi, 39762-5167 USA

Z. Toroczkai

Center for Nonlinear Studies, Theoretical Division, Los Alamos National Laboratory, MS-B258, Los Alamos, New Mexico 87545 USA

Z. Rácz

Institute for Theoretical Physics–HAS, Eötvös University, Pázmány sétány 1/a, 1117 Budapest, Hungary

^*Permanent address: Center for Nonlinear Studies, Theoretical Division, Los Alamos National Laboratory, MS-B258, Los Alamos, NM 87545 USA.

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 73, Iss. 6 — June 2006

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics