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Singletons for Simpletons: Revisiting Windowed Backoff with Chernoff Bounds

Authors Qian M. Zhou, Aiden Calvert, Maxwell Young

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Author Details

Qian M. Zhou
  • Mississippi State University, Department of Mathematics and Statistics, MS, USA
Aiden Calvert
  • Mississippi School for Mathematics and Science, Columbus, MS, USA
Maxwell Young
  • Mississippi State University, Department of Computer Science and Engineering, MS, USA

Funding

  • Young, Maxwell: This research is supported by the National Science Foundation grant CNS 1816076, and by the U.S. National Institute of Justice (NIJ) Grant 2018-75-CX-K002.

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Qian M. Zhou, Aiden Calvert, and Maxwell Young. Singletons for Simpletons: Revisiting Windowed Backoff with Chernoff Bounds. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.FUN.2021.24

Abstract

Backoff algorithms are used in many distributed systems where multiple devices contend for a shared resource. For the classic balls-into-bins problem, the number of singletons - those bins with a single ball - is important to the analysis of several backoff algorithms; however, existing analyses employ advanced probabilistic tools to obtain concentration bounds. Here, we show that standard Chernoff bounds can be used instead, and the simplicity of this approach is illustrated by re-analyzing some well-known backoff algorithms.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Chernoff bounds
  • backoff
  • contention resolution
  • algorithms

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