Balanced Allocations with Heterogeneous Bins: The Power of Memory
Dimitrios Los, Thomas Sauerwald, John Sylvester

TL;DR
This paper demonstrates that the Memory process for load balancing maintains a logarithmic double-logarithmic gap in heterogeneous and heavily loaded settings, outperforming traditional two-choice methods.
Contribution
It extends the analysis of the Memory process to arbitrary load levels and heterogeneous bin distributions, showing it achieves near-optimal gap bounds in complex scenarios.
Findings
Memory process maintains an O(log log n) gap in heterogeneous settings.
Memory process's gap remains bounded independently of m under certain conditions.
A tight O(log n) gap bound is established for a relaxed Memory process with weighted balls.
Abstract
We consider the allocation of balls (jobs) into bins (servers). In the standard Two-Choice process, at each step we first sample two bins uniformly at random and place a ball in the least loaded bin. It is well-known that for any , this results in a gap (difference between the maximum and average load) of (with high probability). In this work, we consider the Memory process [Mitzenmacher, Prabhakar and Shah 2002] where instead of two choices, we only sample one bin per step but we have access to a cache which can store the location of one bin. Mitzenmacher, Prabhakar and Shah showed that in the lightly loaded case (), the Memory process achieves a gap of . Extending the setting of Mitzenmacher et al. in two ways, we first allow the number of balls to be arbitrary, which includes the…
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