Dynamic load balancing for distributed memory multiprocessors
Journal of Parallel and Distributed Computing
Load balancing, selection sorting on the hypercube
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Performance of dynamic load balancing algorithms for unstructured mesh calculations
Concurrency: Practice and Experience
Approximate load balancing on dynamic and asynchronous networks
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
An analysis of diffusive load-balancing
SPAA '94 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures
Randomized algorithms
Mixing of random walks and other diffusions on a graph
Surveys in combinatorics, 1995
Dynamic load balancing by random matchings
Journal of Computer and System Sciences
Simple randomized mergesort on parallel disks
Parallel Computing - Special double issue: parallel I/O
Rapid convergence of a local load balancing algorithm for asynchronous rings
Theoretical Computer Science
Tight Analyses of Two Local Load Balancing Algorithms
SIAM Journal on Computing
An Efficient Algorithm for Perfect Load Balancing on Hypercube Multiprocessors
The Journal of Supercomputing
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
Random Walks on Truncated Cubes and Sampling 0-1 Knapsack Solutions
SIAM Journal on Computing
Load balancing in dynamic structured peer-to-peer systems
Performance Evaluation - P2P computing systems
Simulating a Random Walk with Constant Error
Combinatorics, Probability and Computing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Near-perfect load balancing by randomized rounding
Proceedings of the forty-first annual ACM symposium on Theory of computing
Quasirandom evolutionary algorithms
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Discrete load balancing is (almost) as easy as continuous load balancing
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
The cover time of deterministic random walks
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Sharp bounds by probability-generating functions and variable drift
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Fast simulation of large-scale growth models
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
SIAM Journal on Discrete Mathematics
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
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We propose a simple distributed algorithm for balancing indivisible tokens on graphs. The algorithm is completely deterministic, though it tries to imitate (and enhance) a random algorithm by keeping the accumulated rounding errors as small as possible. Our new algorithm approximates the idealized process (where the tokens are divisible) on important network topologies surprisingly closely. On d-dimensional torus graphs with n nodes it deviates from the idealized process only by an additive constant. In contrast to that, the randomized rounding approach of Friedrich and Sauerwald [8] can deviate up to Ω(polylog n) and the deterministic algorithm of Rabani, Sinclair and Wanka [23] has a deviation of Ω(n1/d). This makes our quasirandom algorithm the first known algorithm for this setting which is optimal both in time and achieved smoothness. We further show that also on the hypercube our algorithm has a smaller deviation from the idealized process than the previous algorithms. To prove these results, we derive several combinatorial and probabilistic results that we believe to be of independent interest. In particular, we show that first-passage probabilities of a random walk on a path with arbitrary weights can be expressed as a convolution of independent geometric probability distributions.