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Minimizing Recourse in an Adaptive Balls and Bins Game

Authors Adi Fine, Haim Kaplan , Uri Stemmer

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LIPIcs.ICALP.2025.77.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Adversary models
  • Theory of computation → Sparsification and spanners
  • Theory of computation → Dynamic graph algorithms
Keywords
  • Adaptive adversary
  • load-balancing game
  • balls-and-bins
  • randomized algorithms
  • dynamic 3-spanner
  • dynamic graph algorithms
  • adversarial robustness

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Abstract

We consider a simple load-balancing game between an algorithm and an adaptive adversary. In a simplified version of this game, the adversary observes the assignment of jobs to machines and selects a machine to kill. The algorithm must then restart the jobs from the failed machine on other machines. The adversary repeats this process, observing the new assignment and eliminating another machine, and so on. The adversary aims to force the algorithm to perform many restarts, while we seek a robust algorithm that minimizes restarts regardless of the adversary’s strategy. This game was recently introduced by Bhattacharya et al. for designing a 3-spanner with low recourse against an adaptive adversary.
We prove that a simple algorithm, which assigns each job to a randomly chosen live bin, incurs O(n log n) recourse against an adaptive adversary. This enables us to construct a much simpler 3-spanner with a recourse that is smaller by a factor of O(log² n) compared to the previous construction, without increasing the update time or the size of the spanner.
This motivates a careful examination of the range of attacks an adaptive adversary can deploy against simple algorithms before resorting to more complex ones. As our case study demonstrates, this attack space may not be as large as it initially appears, enabling the development of robust algorithms that are both simpler and easier to analyze.

Cite As Get BibTex

Adi Fine, Haim Kaplan, and Uri Stemmer. Minimizing Recourse in an Adaptive Balls and Bins Game. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 77:1-77:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.77

Author Details

Adi Fine
  • Blavatnik School of Computer Science, Tel Aviv University, Israel
Haim Kaplan
  • Blavatnik School of Computer Science, Tel Aviv University, Israel
Uri Stemmer
  • Blavatnik School of Computer Science, Tel Aviv University, Israel

Funding

  • Fine, Adi: This work was partially supported by the Israel Science Foundation grant no. 1156/23 and the Blavatnik Family Foundation.
  • Kaplan, Haim: This work was partially supported by the Israel Science Foundation grant no. 1156/23 and the Blavatnik Family Foundation.
  • Stemmer, Uri: This work was partially supported by the Israel Science Foundation grant 1419/24 and the Blavatnik Family Foundation.

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