Proceedings ArticleDOI
Near-perfect load balancing by randomized rounding
Tobias Friedrich,Thomas Sauerwald +1 more
- pp 121-130
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TLDR
It is proved that in comparison to the corresponding model of Rabani, Sinclair, and Wanka (1998) with arbitrary roundings, the randomization yields an improvement of roughly a square root of the achieved discrepancy in the same number of time-steps on all graphs.Abstract:
We consider and analyze a new algorithm for balancing indivisible loads on a distributed network with n processors. The aim is minimizing the discrepancy between the maximum and minimum load. In every time-step paired processors balance their load as evenly as possible. The direction of the excess token is chosen according to a randomized rounding of the participating loads.We prove that in comparison to the corresponding model of Rabani, Sinclair, and Wanka (1998) with arbitrary roundings, the randomization yields an improvement of roughly a square root of the achieved discrepancy in the same number of time-steps on all graphs. For the important case of expanders we can even achieve a constant discrepancy in O(log n (log log n)3) rounds. This is optimal up to loglog-factors while the best previous algorithms in this setting either require ©(log2 n) time or can only achieve a logarithmic discrepancy. Our new result also demonstrates that with randomized rounding the difference between discrete and continuous load balancing vanishes almost completely.read more
Citations
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Journal ArticleDOI
Quasirandom Load Balancing
TL;DR: The quasirandom algorithm, proposed, is the first known algorithm for balancing indivisible tokens on graphs that closely approximates the idealized process (where the tokens are divisible) on important network topologies.
Proceedings ArticleDOI
Parallel rotor walks on finite graphs and applications in discrete load balancing
Hoda Akbari,Petra Berenbrink +1 more
TL;DR: Viewing the parallel rotor walk as a load balancing process, it is proved that the rotor walk falls in the class of bounded-error diffusion processes introduced in [11], which gives discrepancy bounds of O(log3/2 n) and O(1) for hypercube and r-dimensional torus with r=O(1), respectively, which improve over the best existing bounds.
Book ChapterDOI
The cover time of deterministic random walks
TL;DR: The rotor router model is a popular deterministic analogue of a random walk on a graph instead of moving to a random neighbor, the neighbors are served in a fixed order as discussed by the authors.
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Distributed Selfish Load Balancing with Weights and Speeds
TL;DR: In this paper, the authors consider neighborhood load balancing in the context of selfish clients and obtain upper bounds on the expected convergence time towards approximate and exact Nash equilibria, which are significantly better than the previous results in [6].
References
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