Laminar Matroid Secretary: Greedy Strikes Back

Authors Zhiyi Huang , Zahra Parsaeian, Zixuan Zhu



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Author Details

Zhiyi Huang
  • Department of Computer Science, The University of Hong Kong, Hong Kong
Zahra Parsaeian
  • University of Freiburg, Germany
Zixuan Zhu
  • Department of Computer Science, The University of Hong Kong, Hong Kong

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Zhiyi Huang, Zahra Parsaeian, and Zixuan Zhu. Laminar Matroid Secretary: Greedy Strikes Back. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 73:1-73:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ESA.2024.73

Abstract

We show that a simple greedy algorithm is 4.75-competitive for the Laminar Matroid Secretary Problem, improving the 3√3 ≈ 5.196-competitive algorithm based on the forbidden sets technique (Soto, Turkieltaub, and Verdugo, 2018).

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
Keywords
  • Matroid Secretary
  • Greedy Algorithm
  • Laminar Matroid

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References

  1. Moshe Babaioff, Nicole Immorlica, David Kempe, and Robert Kleinberg. Matroid secretary problems. J. ACM, 65(6):35:1-35:26, 2018. URL: https://doi.org/10.1145/3212512.
  2. Moshe Babaioff, Nicole Immorlica, and Robert Kleinberg. Matroids, secretary problems, and online mechanisms. In Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007, New Orleans, Louisiana, USA, January 7-9, 2007, pages 434-443, 2007. URL: http://dl.acm.org/citation.cfm?id=1283383.1283429.
  3. Joseph K Blitzstein and Jessica Hwang. Introduction to probability. Crc Press, 2019. Google Scholar
  4. Evgenii B Dynkin. Optimal choice of the stopping moment of a markov process. In Doklady Akademii Nauk, volume 150, pages 238-240. Russian Academy of Sciences, 1963. Google Scholar
  5. Moran Feldman, Ola Svensson, and Rico Zenklusen. A simple O(log log(rank))-competitive algorithm for the matroid secretary problem. Math. Oper. Res., 43(2):638-650, 2018. URL: https://doi.org/10.1287/MOOR.2017.0876.
  6. Thomas S. Ferguson. Who solved the secretary problem. Statistical Science, 4:282-289, 1989. Google Scholar
  7. Sungjin Im and Yajun Wang. Secretary problems: Laminar matroid and interval scheduling. In Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011, San Francisco, California, USA, January 23-25, 2011, pages 1265-1274, 2011. URL: https://doi.org/10.1137/1.9781611973082.96.
  8. Patrick Jaillet, José A. Soto, and Rico Zenklusen. Advances on matroid secretary problems: Free order model and laminar case. In Integer Programming and Combinatorial Optimization - 16th International Conference, IPCO 2013, Valparaíso, Chile, March 18-20, 2013. Proceedings, pages 254-265, 2013. URL: https://doi.org/10.1007/978-3-642-36694-9_22.
  9. Thomas Kesselheim, Klaus Radke, Andreas Tönnis, and Berthold Vöcking. An optimal online algorithm for weighted bipartite matching and extensions to combinatorial auctions. In Algorithms - ESA 2013 - 21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings, pages 589-600, 2013. URL: https://doi.org/10.1007/978-3-642-40450-4_50.
  10. Oded Lachish. O(log log rank) competitive ratio for the matroid secretary problem. In 55th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2014, Philadelphia, PA, USA, October 18-21, 2014, pages 326-335, 2014. URL: https://doi.org/10.1109/FOCS.2014.42.
  11. Dennis V. Lindley. Dynamic programming and decision theory. Journal of The Royal Statistical Society Series C-applied Statistics, 10:39-51, 1961. Google Scholar
  12. Tengyu Ma, Bo Tang, and Yajun Wang. The simulated greedy algorithm for several submodular matroid secretary problems. Theory Comput. Syst., 58(4):681-706, 2016. URL: https://doi.org/10.1007/S00224-015-9642-4.
  13. James G Oxley. Matroid Theory. Oxford University Press, 2006. Google Scholar
  14. Alexander Schrijver. Combinatorial optimization: polyhedra and efficiency, volume 24. Springer, 2003. Google Scholar
  15. José A. Soto, Abner Turkieltaub, and Victor Verdugo. Strong algorithms for the ordinal matroid secretary problem. Math. Oper. Res., 46(2):642-673, 2021. URL: https://doi.org/10.1287/MOOR.2020.1083.
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