Laminar Matroid Secretary: Greedy Strikes Back
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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

Funding

This work is supported by General Research Fund from Research Grants Council of Hong Kong (Grand No. 17211723).

Cite As Get BibTex

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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Supplementary Materials

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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