Dynamic diffusion load balancing

Berenbrink, P.; Friedetzky, T.; Martin, R.

Abstract

We consider the problem of dynamic load balancing in arbitrary (connected) networks on n nodes. Our load generation model is such that during each round, n tasks are generated on arbitrary nodes, and then (possibly after some balancing) one task is deleted from every non-empty node. Notice that this model fully saturates the resources of the network in the sense that we generate just as many new tasks per round as the network is able to delete. We show that even in this situation the system is stable, in that the total load remains bounded (as a function of n alone) over time. Our proof only requires that the underlying “communication” graph be connected. (It of course also works if we generate less than n new tasks per round, but the major contribution of this paper is the fully saturated case.) We further show that the upper bound we obtain is asymptotically tight (up to a moderate multiplicative constant) by demonstrating a corresponding lower bound on the system load for the particular example of a linear array (or path). We also show some simple negative results (i.e., instability) for work-stealing based diffusion-type algorithms in this setting.

Citation

Berenbrink, P., Friedetzky, T., & Martin, R. (2005, July). Dynamic diffusion load balancing. Presented at 32nd International Colloquium on Automata, Languages and Programming : ICALP 2005, Lisboa, Portugal

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 32nd International Colloquium on Automata, Languages and Programming : ICALP 2005
• Start Date: Jul 11, 2005
• End Date: Jul 15, 2005
• Publication Date: 2005-07
• Deposit Date: Nov 4, 2008
• Publicly Available Date: Nov 4, 2008
• Print ISSN: 0302-9743
• Peer Reviewed: Peer Reviewed
• Pages: 1386-1398
• Series Title: Lecture notes in computer science
• Series Number: 3580
• Series ISSN: 0302-9743,1611-3349
• Book Title: Automata, languages and programming : 32nd International Colloquium, ICALP 2005, 11-15 July 2005, Lisbon, Portugal ; proceedings
• ISBN: 9783540275800
• DOI: https://doi.org/10.1007/11523468_112
• Keywords: Network, Algorithm, Load generation model.
• Public URL: https://durham-repository.worktribe.com/output/1680127
• Publisher URL: http://springerlink.metapress.com/link.asp?id=bn60fter0q68whlq
• Additional Information: July 11-15, 2005.