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Load Balancing Under Adaptive Bin Deletions

Authors Haim Kaplan , Shay Sapir , Uri Stemmer

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Subject Classification

ACM Subject Classification
  • Theory of computation → Adversary models
  • Theory of computation → Randomness, geometry and discrete structures
Keywords
  • Balls and Bins
  • Adaptive Adversary

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Abstract

We analyze a balls-and-bins game against an adaptive adversary that sequentially deletes bins. Starting with n balls distributed across n bins, the adversary deletes a bin in each step, forcing the algorithm to redistribute its balls to surviving bins. We prove that after n/2 rounds, uniform random redistribution yields optimal O(n) recourse and O((log n)/(log log n)) maximum load. Furthermore, we show that applying the "power of two choices" reduces the maximum load to O(log log n) while maintaining linear recourse. 
We also consider a variation of this game where the balls from the deleted bin are partitioned evenly among d ≪ n random bins rather than being redistributed independently. We demonstrate that keeping the balls together (d = 1), which gives small maximum load and recourse against an oblivious adversary, fails against an adaptive adversary. Nevertheless, we show that splitting the balls into just two groups (d = 2) is sufficient to recover linear recourse and efficient load balancing in the adaptive setting.

Cite As Get BibTex

Haim Kaplan, Shay Sapir, and Uri Stemmer. Load Balancing Under Adaptive Bin Deletions. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 54:1-54:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2026.54

Author Details

Haim Kaplan
  • Tel Aviv University, Israel
  • Google Research, Tel Aviv, Israel
Shay Sapir
  • Weizmann Institute, Rehovot, Israel
  • Google Research, Tel Aviv, Israel
Uri Stemmer
  • Tel Aviv University, Israel
  • Google Research, Tel Aviv, Israel

Funding

  • Kaplan, Haim: Partially supported by the Israel Science Foundation (grant 1156/23), and the Blavatnik Research Foundation.
  • Stemmer, Uri: Partially supported by the Israel Science Foundation (grant 1419/24), and the Blavatnik Research Foundation.

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