Balanced Allocations: Caching and Packing, Twinning and Thinning

@article{Los2022BalancedAC,
  title={Balanced Allocations: Caching and Packing, Twinning and Thinning},
  author={Dimitrios Los and Thomas Sauerwald and John Sylvester},
  journal={ArXiv},
  year={2022},
  volume={abs/2110.10759}
}
We consider the sequential allocation of $m$ balls (jobs) into $n$ bins (servers) by allowing each ball to choose from some bins sampled uniformly at random. The goal is to maintain a small gap between the maximum load and the average load. In this paper, we present a general framework that allows us to analyze various allocation processes that slightly prefer allocating into underloaded, as opposed to overloaded bins. Our analysis covers several natural instances of processes, including: The… 
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Balanced Allocation on Hypergraphs
TLDR
The notion of pair visibility is introduced and popular d-choice allocation algorithms with related choices including graphs andhypergraphs models are studied, establishing a lower bound for the maximum load attained by the balanced allocation for a sequence of hypergraphs in terms of Pair visibility.