LIPIcs.ICALP.2021.103.pdf
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Matching on the Line Admits No o(√log n)-Competitive Algorithm
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48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Colloquium on Automata, Languages, and Programming (ICALP) - License:
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- Publication Date: 2021-07-02
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Acknowledgements
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)
https://doi.org/10.4230/LIPIcs.ICALP.2021.103
https://doi.org/10.4230/LIPIcs.ICALP.2021.103
Abstract
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
Keywords
- Metric matching
- online algorithms
- competitive analysis
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References
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Antonios Antoniadis, Neal Barcelo, Michael Nugent, Kirk Pruhs, and Michele Scquizzato. A o(n)-competitive deterministic algorithm for online matching on a line. Algorithmica, 81(7):2917-2933, 2019.
-
Antonios Antoniadis, Christian Coester, Marek Eliás, Adam Polak, and Bertrand Simon. Online metric algorithms with untrusted predictions. In Proceedings of the 37th ICML, pages 345-355, 2020.
-
Antonios Antoniadis, Carsten Fischer, and Andreas Tönnis. A collection of lower bounds for online matching on the line. In Proceedings of the 13th LATIN, pages 52-65, 2018.
-
Bernhard Fuchs, Winfried Hochstättler, and Walter Kern. Online matching on a line. Theor. Comput. Sci., 332(1-3):251-264, 2005.
-
Anupam Gupta and Kevin Lewi. The online metric matching problem for doubling metrics. In Proceedings of the 39th ICALP, pages 424-435, 2012.
-
Varun Gupta, Ravishankar Krishnaswamy, and Sai Sandeep. Permutation strikes back: The power of recourse in online metric matching. In Proceedings of the 23rd APPROX, pages 40:1-40:20, 2020.
-
Bala Kalyanasundaram and Kirk Pruhs. Online weighted matching. J. Algorithms, 14(3):478-488, 1993.
-
Bala Kalyanasundaram and Kirk Pruhs. Online network optimization problems. In Online Algorithms: The State of the Art, pages 268-280. Springer-Verlag, 1998. From the Dagstuhl Seminar on Online Algorithms, 1996.
-
Samir Khuller, Stephen G. Mitchell, and Vijay V. Vazirani. On-line algorithms for weighted bipartite matching and stable marriages. Theor. Comput. Sci., 127(2):255-267, 1994.
-
Elias Koutsoupias and Akash Nanavati. The online matching problem on a line. In Proceedings of the 1st WAOA, pages 179-191, 2003.
-
Nicole Megow and Lukas Nölke. Online minimum cost matching with recourse on the line. In Proceedings of the 23rd APPROX, pages 37:1-37:16, 2020.
-
Krati Nayyar and Sharath Raghvendra. An input sensitive online algorithm for the metric bipartite matching problem. In Proceedings of the 58th IEEE FOCS, pages 505-515, 2017.
-
Sharath Raghvendra. Optimal analysis of an online algorithm for the bipartite matching problem on a line. In Proceedings of the 34th SoCG, pages 67:1-67:14, 2018.
-
Rob van Stee. SIGACT news online algorithms column 27: Online matching on the line, part 1. SIGACT News, 47(1):99-110, 2016.