Dynamic load balancing for distributed memory multiprocessors
Journal of Parallel and Distributed Computing
Load balancing and Poisson equation in a graph
Concurrency: Practice and Experience
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
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
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
Simulating a Random Walk with Constant Error
Combinatorics, Probability and Computing
Deterministic random walks on the two-dimensional grid
Combinatorics, Probability and Computing
Near-perfect load balancing by randomized rounding
Proceedings of the forty-first annual ACM symposium on Theory of computing
Concentration of Measure for the Analysis of Randomized Algorithms
Concentration of Measure for the Analysis of Randomized Algorithms
Discrete load balancing is (almost) as easy as continuous load balancing
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
SODA '10 Proceedings of the twenty-first 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
Parallel rotor walks on finite graphs and applications in discrete load balancing
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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We present a new randomized diffusion-based algorithm for balancing indivisible tasks (tokens) on a network. Our aim is to minimize the discrepancy between the maximum and minimum load. The algorithm works as follows. Every vertex distributes its tokens as evenly as possible among its neighbors and itself. If this is not possible without splitting some tokens, the vertex redistributes its excess tokens among all its neighbors randomly (without replacement). In this paper we prove several upper bounds on the load discrepancy for general networks. These bounds depend on some expansion properties of the network, that is, the second largest eigenvalue, and a novel measure which we refer to as refined local divergence. We then apply these general bounds to obtain results for some specific networks. For constant-degree expanders and torus graphs, these yield exponential improvements on the discrepancy bounds compared to the algorithm of Rabani, Sinclair, and Wanka [14]. For hypercubes we obtain a polynomial improvement. In contrast to previous papers, our algorithm is vertex-based and not edge-based. This means excess tokens are assigned to vertices instead to edges, and the vertex reallocates all of its excess tokens by itself. This approach avoids nodes having "negative loads" (like in [8, 10]), but causes additional dependencies for the analysis.