Matching on the Line Admits No o(√log n)-Competitive Algorithm

Authors Enoch Peserico, Michele Scquizzato

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Enoch Peserico
  • Università degli Studi di Padova, Italy
Michele Scquizzato
  • Università degli Studi di Padova, Italy


We are indebted to Kirk Pruhs and the anonymous reviewers for their constructive criticism and insightful observations.

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Enoch Peserico and Michele Scquizzato. Matching on the Line Admits No o(√log n)-Competitive Algorithm. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 103:1-103:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We present a simple proof that the competitive ratio of any randomized online matching algorithm for the line exceeds √{log₂(n +1)}/15 for all n = 2ⁱ-1: i ∈ ℕ, settling a 25-year-old open question.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Metric matching
  • online algorithms
  • competitive analysis


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