Local divergence of Markov chains and the analysis of iterative load-balancing schemes

Yuval Rabani*, Alistair Sinclair, Rolf Wanka

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

121 Scopus citations

Abstract

We develop a general technique for the quantitative analysis of iterative distributed load balancing schemes. We illustrate the technique by studying two simple, intuitively appealing models that are prevalent in the literature: the diffusive paradigm, and periodic balancing circuits (or the dimension exchange paradigm). It is well known that such load balancing schemes can be roughly modeled by Markov chains, but also that this approximation can be quite inaccurate. Our main contribution is an effective way of characterizing the deviation between the actual loads and the distribution generated by a related Markov chain, in terms of a natural quantity which we call the local divergence. We apply this technique to obtain bounds on the number of rounds required to achieve coarse balancing in general networks, cycles and meshes in these models. For balancing circuits, we also present bounds for the stronger requirement of perfect balancing, or counting.

Original languageAmerican English
Pages (from-to)694-703
Number of pages10
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
StatePublished - 1998
Externally publishedYes
EventProceedings of the 1998 39th Annual Symposium on Foundations of Computer Science - Palo Alto, CA, USA
Duration: 8 Nov 199811 Nov 1998

Fingerprint

Dive into the research topics of 'Local divergence of Markov chains and the analysis of iterative load-balancing schemes'. Together they form a unique fingerprint.

Cite this