Document Open Access Logo

Making Three out of Two: Three-Way Online Correlated Selection

Authors Yongho Shin, Hyung-Chan An

PDF
Thumbnail PDF

File

LIPIcs.ISAAC.2021.49.pdf
  • Filesize: 0.78 MB
  • 17 pages

Document Identifiers

Author Details

Yongho Shin
  • Department of Computer Science, Yonsei University, Seoul, South Korea
Hyung-Chan An
  • Department of Computer Science, Yonsei University, Seoul, South Korea

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2019R1C1C1008934).

Acknowledgements

We thank the anonymous reviewers for their helpful comments.

Cite As Get BibTex

Yongho Shin and Hyung-Chan An. Making Three out of Two: Three-Way Online Correlated Selection. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 49:1-49:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ISAAC.2021.49

Abstract

Two-way online correlated selection (two-way OCS) is an online algorithm that, at each timestep, takes a pair of elements from the ground set and irrevocably chooses one of the two elements, while ensuring negative correlation in the algorithm's choices. Whilst OCS was initially invented by Fahrbach, Huang, Tao, and Zadimoghaddam to break a natural long-standing barrier in the edge-weighted online bipartite matching problem, it is an interesting technique on its own due to its capability of introducing a powerful algorithmic tool, namely negative correlation, to online algorithms. As such, Fahrbach et al. posed two tantalizing open questions in their paper, one of which was the following: Can we obtain n-way OCS for n > 2, in which the algorithm can be given n > 2 elements to choose from at each timestep?
In this paper, we affirmatively answer this open question by presenting a three-way OCS. Our algorithm uses two-way OCS as its building block and is simple to describe; however, as it internally runs two instances of two-way OCS, one of which is fed with the output of the other, the final output probability distribution becomes highly elusive. We tackle this difficulty by approximating the output distribution of OCS by a flat, less correlated function and using it as a safe "surrogate" of the real distribution. Our three-way OCS also yields a 0.5093-competitive algorithm for edge-weighted online matching, demonstrating its usefulness.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
Keywords
  • online correlated selection
  • multi-way OCS
  • online algorithms
  • negative correlation
  • edge-weighted online bipartite matching

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Gagan Aggarwal, Gagan Goel, Chinmay Karande, and Aranyak Mehta. Online vertex-weighted bipartite matching and single-bid budgeted allocations. In Symposium on Discrete Algorithms (SODA), pages 1253-1264. SIAM, 2011. Google Scholar
  2. Arash Asadpour, Michel X Goemans, Aleksander Mądry, Shayan Oveis Gharan, and Amin Saberi. An O(log n/log log n)-approximation algorithm for the asymmetric traveling salesman problem. Operations Research, 65(4):1043-1061, 2017. Google Scholar
  3. Itai Ashlagi, Maximilien Burq, Chinmoy Dutta, Patrick Jaillet, Amin Saberi, and Chris Sholley. Edge weighted online windowed matching. In Conference on Economics and Computation (EC), pages 729-742, 2019. Google Scholar
  4. Benjamin E. Birnbaum and Claire Mathieu. On-line bipartite matching made simple. SIGACT News, 39(1):80-87, 2008. Google Scholar
  5. Guy Blanc and Moses Charikar. Multiway online correlated selection. arXiv preprint, 2021. To appear in Symposium on Foundations of Computer Science (FOCS 2021). URL: http://arxiv.org/abs/2106.05579.
  6. Brian Brubach, Karthik Abinav Sankararaman, Aravind Srinivasan, and Pan Xu. New algorithms, better bounds, and a novel model for online stochastic matching. In European Symposium on Algorithms (ESA). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2016. Google Scholar
  7. Chandra Chekuri and Jan Vondrák. Randomized pipage rounding for matroid polytopes and applications. CoRR, abs/0909.4348, 2009. URL: http://arxiv.org/abs/0909.4348.
  8. Nikhil R. Devanur, Kamal Jain, and Robert D. Kleinberg. Randomized primal-dual analysis of RANKING for online bipartite matching. In Symposium on Discrete Algorithms (SODA), pages 101-107. SIAM, 2013. Google Scholar
  9. Alon Eden, Michal Feldman, Amos Fiat, and Kineret Segal. An economics-based analysis of ranking for online bipartite matching. In Symposium on Simplicity in Algorithms (SOSA), pages 107-110. SIAM, 2021. Google Scholar
  10. Matthew Fahrbach, Zhiyi Huang, Runzhou Tao, and Morteza Zadimoghaddam. Edge-weighted online bipartite matching. In Symposium on Foundations of Computer Science (FOCS), pages 412-423. IEEE, 2020. Google Scholar
  11. Jon Feldman, Nitish Korula, Vahab Mirrokni, Shanmugavelayutham Muthukrishnan, and Martin Pál. Online ad assignment with free disposal. In International Workshop on Internet and Network Economics (WINE), pages 374-385. Springer, 2009. Google Scholar
  12. Jon Feldman, Aranyak Mehta, Vahab Mirrokni, and Shan Muthukrishnan. Online stochastic matching: Beating 1-1/e. In Symposium on Foundations of Computer Science (FOCS), pages 117-126. IEEE, 2009. Google Scholar
  13. Buddhima Gamlath, Sagar Kale, and Ola Svensson. Beating greedy for stochastic bipartite matching. In Symposium on Discrete Algorithms (SODA), pages 2841-2854. SIAM, 2019. Google Scholar
  14. Buddhima Gamlath, Michael Kapralov, Andreas Maggiori, Ola Svensson, and David Wajc. Online matching with general arrivals. In Symposium on Foundations of Computer Science (FOCS), pages 26-37. IEEE, 2019. Google Scholar
  15. Ruiquan Gao, Zhongtian He, Zhiyi Huang, Zipei Nie, Bijun Yuan, and Yan Zhong. Improved online correlated selection. arXiv preprint, 2021. To appear in Symposium on Foundations of Computer Science (FOCS 2021). URL: http://arxiv.org/abs/2106.04224.
  16. Gagan Goel and Aranyak Mehta. Online budgeted matching in random input models with applications to adwords. In Symposium on Discrete Algorithms (SODA), pages 982-991. SIAM, 2008. Google Scholar
  17. Bernhard Haeupler, Vahab S Mirrokni, and Morteza Zadimoghaddam. Online stochastic weighted matching: Improved approximation algorithms. In International Workshop on Internet and Network Economics(WINE), pages 170-181. Springer, 2011. Google Scholar
  18. Zhiyi Huang, Ning Kang, Zhihao Gavin Tang, Xiaowei Wu, Yuhao Zhang, and Xue Zhu. Fully online matching. Journal of the ACM, 67(3):1-25, 2020. Google Scholar
  19. Zhiyi Huang, Binghui Peng, Zhihao Gavin Tang, Runzhou Tao, Xiaowei Wu, and Yuhao Zhang. Tight competitive ratios of classic matching algorithms in the fully online model. In Symposium on Discrete Algorithms (SODA), pages 2875-2886. SIAM, 2019. Google Scholar
  20. Zhiyi Huang and Xinkai Shu. Online stochastic matching, poisson arrivals, and the natural linear program. In Symposium on Theory of Computing (STOC), pages 682-693. ACM, 2021. Google Scholar
  21. Zhiyi Huang, Zhihao Gavin Tang, Xiaowei Wu, and Yuhao Zhang. Online vertex-weighted bipartite matching: Beating 1-1/e with random arrivals. ACM Transactions on Algorithms, 15(3):1-15, 2019. Google Scholar
  22. Zhiyi Huang, Zhihao Gavin Tang, Xiaowei Wu, and Yuhao Zhang. Fully online matching ii: Beating ranking and water-filling. In Symposium on Foundations of Computer Science (FOCS), pages 1380-1391. IEEE, 2020. Google Scholar
  23. Zhiyi Huang, Qiankun Zhang, and Yuhao Zhang. Adwords in a panorama. In Symposium on Foundations of Computer Science (FOCS), pages 1416-1426. IEEE, 2020. Google Scholar
  24. Bala Kalyanasundaram and Kirk Pruhs. Online weighted matching. Journal of Algorithms, 14(3):478-488, 1993. Google Scholar
  25. Richard M Karp, Umesh V Vazirani, and Vijay V Vazirani. An optimal algorithm for on-line bipartite matching. In Symposium on Theory of Computing (STOC), pages 352-358. ACM, 1990. Google Scholar
  26. Thomas Kesselheim, Klaus Radke, Andreas Tönnis, and Berthold Vöcking. An optimal online algorithm for weighted bipartite matching and extensions to combinatorial auctions. In European Symposium on Algorithms (ESA), pages 589-600. Springer, 2013. Google Scholar
  27. Samir Khuller, Stephen G Mitchell, and Vijay V Vazirani. On-line algorithms for weighted bipartite matching and stable marriages. Theoretical Computer Science, 127(2):255-267, 1994. Google Scholar
  28. Nitish Korula, Vahab S Mirrokni, and Morteza Zadimoghaddam. Bicriteria online matching: Maximizing weight and cardinality. In International Conference on Web and Internet Economics (WINE), pages 305-318. Springer, 2013. Google Scholar
  29. Vahideh H Manshadi, Shayan Oveis Gharan, and Amin Saberi. Online stochastic matching: Online actions based on offline statistics. Mathematics of Operations Research, 37(4):559-573, 2012. Google Scholar
  30. Aranyak Mehta. Online matching and ad allocation. Foundations and Trends in Theoretical Computer Science, 8(4):265-368, 2013. Google Scholar
  31. Aranyak Mehta, Amin Saberi, Umesh Vazirani, and Vijay Vazirani. Adwords and generalized online matching. Journal of the ACM, 54(5):22, 2007. Google Scholar
  32. Aranyak Mehta, Bo Waggoner, and Morteza Zadimoghaddam. Online stochastic matching with unequal probabilities. In Symposium on Discrete Algorithms (SODA), pages 1388-1404. SIAM, 2015. Google Scholar
  33. Yongho Shin and Hyung-Chan An. Making three out of two: Three-way online correlated selection. arXiv preprint, 2021. URL: http://arxiv.org/abs/2107.02605.
  34. Aravind Srinivasan. Distributions on level-sets with applications to approximation algorithms. In Symposium on Foundations of Computer Science (FOCS), pages 588-597. IEEE, 2001. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact