Balanced Allocations with the Choice of Noise

06/15/2022
by   Dimitrios Los, et al.
0

We consider the allocation of m balls (jobs) into n bins (servers). In the standard Two-Choice process, at each step t=1,2,…,m we first sample two randomly chosen bins, compare their two loads and then place a ball in the least loaded bin. It is well-known that for any m ≥ n, this results in a gap (difference between the maximum and average load) of log_2 log n + Θ(1) (with high probability). In this work, we consider Two-Choice in different models with noisy load comparisons. One key model involves an adaptive adversary whose power is limited by some threshold g ∈ℕ. In each round, such adversary can determine the result of any load comparison between two bins whose loads differ by at most g, while if the load difference is greater than g, the comparison is correct. For this adversarial model, we first prove that for any m ≥ n the gap is O(g+log n) with high probability. Then through a refined analysis we prove that if g ≤log n, then for any m ≥ n the gap is O(g/log g·loglog n). For constant values of g, this generalizes the heavily loaded analysis of [BCSV06, TW14] for the Two-Choice process, and establishes that asymptotically the same gap bound holds even if many (or possibly all) load comparisons among "similarly loaded" bins are wrong. Finally, we complement these upper bounds with tight lower bounds, which establishes an interesting phase transition on how the parameter g impacts the gap. We also apply a similar analysis to other noise models, including ones where bins only update their load information with delay. For example, for the model of [BCEFN12] where balls are allocated in consecutive batches of size n, we present an improved and tight gap bound of Θ(log n/ loglog n ).

READ FULL TEXT
research
01/24/2023

Balanced Allocations with Heterogeneous Bins: The Power of Memory

We consider the allocation of m balls (jobs) into n bins (servers). In t...
research
04/08/2022

The Power of Filling in Balanced Allocations

It is well known that if m balls (jobs) are placed sequentially into n b...
research
02/09/2023

Balanced Allocations in Batches: The Tower of Two Choices

In balanced allocations, the goal is to place m balls into n bins, so as...
research
03/25/2022

Balanced Allocations in Batches: Simplified and Generalized

We consider the allocation of m balls (jobs) into n bins (servers). In t...
research
07/08/2021

Balanced Allocations with Incomplete Information: The Power of Two Queries

We consider the problem of allocating m balls into n bins with incomplet...
research
06/10/2021

Well-Balanced Allocation on General Graphs

We study the graphical generalization of the 2-choice balls-into-bins pr...
research
03/20/2020

Dynamic Averaging Load Balancing on Cycles

We consider the following dynamic load-balancing process: given an under...

Please sign up or login with your details

Forgot password? Click here to reset