Dynamic load balancing for distributed memory multiprocessors
Journal of Parallel and Distributed Computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
An analysis of diffusive load-balancing
SPAA '94 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures
Mixing of random walks and other diffusions on a graph
Surveys in combinatorics, 1995
A Chernoff Bound for Random Walks on Expander Graphs
SIAM Journal on Computing
Efficient schemes for nearest neighbor load balancing
Parallel Computing - Special issue on parallelization techniques for numerical modelling
Tight Analyses of Two Local Load Balancing Algorithms
SIAM Journal on Computing
Load balancing of unit size tokens and expansion properties of graphs
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Local Divergence of Markov Chains and the Analysis of Iterative Load-Balancing Schemes
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Near-perfect load balancing by randomized rounding
Proceedings of the forty-first annual ACM symposium on Theory of computing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Randomized diffusion for indivisible loads
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A simple approach for adapting continuous load balancing processes to discrete settings
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Brief announcement: threshold load balancing in networks
Proceedings of the 2013 ACM symposium on Principles of distributed computing
| Hi-index | 0.00 |
We consider the problem of diffusion-based load balancing on a distributed network with n processors. If the load is arbitrarily divisible, then the convergence is fairly well captured in terms of the second largest eigenvalue of the diffusion matrix. As for many applications load can not be arbitrarily divided, we consider a model where load consists of indivisible, unit-size tokens. Quantifying by how much this integrality assumption worsens the efficiency of load balancing algorithms is a natural question which has been posed by many authors [9, 15, 16, 6, 19, 17]. In this paper we show essentially that discrete load balancing is almost as easy as continuous load balancing. More precisely, we present a fully distributed, randomized algorithm for discrete load balancing that balances the load up to an additive constant error on any graph in time O(log (Kn)/(1-λ2)), where K is the initial imbalance and λ2 is the second largest eigenvalue of the diffusion matrix. This improves and tightens a result of Elsässer, Monien, Schamberger (2006) who proved a runtime bound of O((log (K) + (log n)2) / (1-λ2)). We also develop a load balancing algorithm based on routing that achieves a runtime of O(D ⋅ log n), where D is the diameter of the graph.