Proceedings ArticleDOI
Near-perfect load balancing by randomized rounding
Tobias Friedrich,Thomas Sauerwald +1 more
- pp 121-130
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
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Threshold Load Balancing in Networks
Martin Hoefer,Thomas Sauerwald +1 more
TL;DR: It is shown that convergence is achieved in a number of rounds that is only logarithmic in m and polynomial in structural properties of the graph, and even when migration is fully controlled by users, protocols obtain rapid convergence to approximately balanced states.
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Improved Analysis of Deterministic Load-Balancing Schemes
TL;DR: It is proved that algorithms which are cumulatively fair and where every node retains a sufficient part of its load in each step, achieve a discrepancy of O(d√log n/μ, d√n) in time O(T), and that in general neither of these assumptions may be omitted without increasing discrepancy.
Proceedings ArticleDOI
Discrete Load Balancing in Heterogeneous Networks with a Focus on Second-Order Diffusion
TL;DR: A framework for randomly rounding the flow generated by continuous diffusion schemes over the edges of a graph in order to obtain corresponding discrete schemes and a bound for the minimum initial load in a network that is sufficient to prevent the occurrence of negative load during the execution of second order diffusion schemes are provided.
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Balancing indivisible real-valued loads in arbitrary networks
TL;DR: This work proposes a novel algorithm for dynamic balancing of indivisible, real-valued loads, and indicates that the increased communication cost of the proposed algorithm is compensated by a higher solution quality, leading on average to about an order of magnitude gain in overall performance.
Proceedings ArticleDOI
Gossip vs. Markov chains, and randomness-efficient rumor spreading
TL;DR: This work establishes a new connection between the rumor spreading process in an arbitrary graph and certain Markov chains, and establishes a reduction from rumor spreading processes to branching programs, and shows that, for many graph families, O(poly log n) random bits in total suffice for fast rumor spreading.
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