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Competitive Query Minimization for Stable Matching with One-Sided Uncertainty

Authors Evripidis Bampis , Konstantinos Dogeas , Thomas Erlebach , Nicole Megow , Jens Schlöter , Amitabh Trehan

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Author Details

Evripidis Bampis
  • Sorbonne Université, CNRS, LIP6, Paris, France
Konstantinos Dogeas
  • Department of Computer Science, Durham University, Durham, United Kingdom
Thomas Erlebach
  • Department of Computer Science, Durham University, Durham, United Kingdom
Nicole Megow
  • Faculty of Mathematics and Computer Science, University of Bremen, Bremen, Germany
Jens Schlöter
  • Faculty of Mathematics and Computer Science, University of Bremen, Bremen, Germany
Amitabh Trehan
  • Department of Computer Science, Durham University, Durham, United Kingdom

Funding

This research was supported by EPSRC grant EP/S033483/2.
  • Bampis, Evripidis: Partially funded by the grant ANR-19-CE48-0016 from the French National Research Agency (ANR).
  • Megow, Nicole: Supported by DFG grant no. 517912373.

Cite AsGet BibTex

Evripidis Bampis, Konstantinos Dogeas, Thomas Erlebach, Nicole Megow, Jens Schlöter, and Amitabh Trehan. Competitive Query Minimization for Stable Matching with One-Sided Uncertainty. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 17:1-17:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.17

Abstract

We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are unknown. An algorithm can make queries to reveal information about the preferences of the agents in B. We examine three query models: comparison queries, interviews, and set queries. Using competitive analysis, our aim is to design algorithms that minimize the number of queries required to solve the problem of finding a stable matching or verifying that a given matching is stable (or stable and optimal for the agents of one side). We present various upper and lower bounds on the best possible competitive ratio as well as results regarding the complexity of the offline problem of determining the optimal query set given full information.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Matching under Preferences
  • Stable Marriage
  • Query-Competitive Algorithms
  • Uncertainty

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References

  1. Haris Aziz, Péter Biró, Ronald de Haan, and Baharak Rastegari. Pareto optimal allocation under uncertain preferences: uncertainty models, algorithms, and complexity. Artif. Intell., 276:57-78, 2019. Google Scholar
  2. Haris Aziz, Péter Biró, Serge Gaspers, Ronald de Haan, Nicholas Mattei, and Baharak Rastegari. Stable matching with uncertain linear preferences. Algorithmica, 82(5):1410-1433, 2020. Google Scholar
  3. Evripidis Bampis, Konstantinos Dogeas, Thomas Erlebach, Nicole Megow, Jens Schlöter, and Amitabh Trehan. Competitive query minimization for stable matching with one-sided uncertainty, 2024. URL: https://arxiv.org/abs/2407.10170.
  4. Evripidis Bampis, Christoph Dürr, Thomas Erlebach, Murilo Santos de Lima, Nicole Megow, and Jens Schlöter. Orienting (hyper)graphs under explorable stochastic uncertainty. In ESA, volume 204 of LIPIcs, pages 10:1-10:18, 2021. URL: https://doi.org/10.4230/LIPIcs.ESA.2021.10.
  5. Allan Borodin and Ran El-Yaniv. Online computation and competitive analysis. Cambridge University Press, 1998. Google Scholar
  6. Joanna Drummond and Craig Boutilier. Elicitation and approximately stable matching with partial preferences. In IJCAI, pages 97-105. IJCAI/AAAI, 2013. Google Scholar
  7. Joanna Drummond and Craig Boutilier. Preference elicitation and interview minimization in stable matchings. In AAAI, pages 645-653. AAAI Press, 2014. Google Scholar
  8. Christoph Dürr, Thomas Erlebach, Nicole Megow, and Julie Meißner. An adversarial model for scheduling with testing. Algorithmica, 82(12):3630-3675, 2020. Google Scholar
  9. Lars Ehlers and Jordi Massó. Matching markets under (in)complete information. J. Econ. Theory, 157:295-314, 2015. Google Scholar
  10. T. Erlebach and M. Hoffmann. Query-competitive algorithms for computing with uncertainty. Bulletin of the EATCS, 116:22-39, 2015. URL: http://bulletin.eatcs.org/index.php/beatcs/article/view/335.
  11. Thomas Erlebach, Murilo S. de Lima, Nicole Megow, and Jens Schlöter. Sorting and hypergraph orientation under uncertainty with predictions. In IJCAI, pages 5577-5585. ijcai.org, 2023. Google Scholar
  12. Guy Even, Joseph Naor, Baruch Schieber, and Madhu Sudan. Approximating minimum feedback sets and multicuts in directed graphs. Algorithmica, 20(2):151-174, 1998. Google Scholar
  13. D. Gale and L. S. Shapley. College admissions and the stability of marriage. The American Mathematical Monthly, 69(1):9-15, 1962. URL: https://doi.org/10.1080/00029890.1962.11989827.
  14. Yannai A. Gonczarowski, Noam Nisan, Rafail Ostrovsky, and Will Rosenbaum. A stable marriage requires communication. Games Econ. Behav., 118:626-647, 2019. URL: https://doi.org/10.1016/j.geb.2018.10.013.
  15. Dan Gusfield and Robert W. Irving. The Stable Marriage Problem - Structure and Algorithms. Foundations of computing series. MIT Press, 1989. Google Scholar
  16. Guillaume Haeringer and Vincent Iehlé. Two-sided matching with one-sided preferences. In EC, page 353. ACM, 2014. Google Scholar
  17. Guillaume Haeringer and Vincent Iehlé. Two-sided matching with (almost) one-sided preferences. American Economic Journal: Microeconomics, 11(3):155-190, 2019. Google Scholar
  18. Guillaume Haeringer and Vincent Iehlé. Enjeux stratégiques du concours de recrutement des enseignants chercheurs. Revue Economique, 61(4):697-721, 2010. Google Scholar
  19. M. M. Halldórsson and M. S. de Lima. Query-competitive sorting with uncertainty. In MFCS, volume 138 of LIPIcs, pages 7:1-7:15, 2019. URL: https://doi.org/10.4230/LIPIcs.MFCS.2019.7.
  20. Michael Hoffmann, Thomas Erlebach, Danny Krizanc, Matús Mihalák, and Rajeev Raman. Computing minimum spanning trees with uncertainty. In STACS, volume 1 of LIPIcs, pages 277-288. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Germany, 2008. Google Scholar
  21. Hadi Hosseini, Vijay Menon, Nisarg Shah, and Sujoy Sikdar. Necessarily optimal one-sided matchings. In AAAI, pages 5481-5488. AAAI Press, 2021. Google Scholar
  22. S. Kahan. A model for data in motion. In STOC'91: 23rd Annual ACM Symposium on Theory of Computing, pages 265-277, 1991. URL: https://doi.org/10.1145/103418.103449.
  23. Richard M. Karp. Reducibility among combinatorial problems. In 50 Years of Integer Programming, pages 219-241. Springer, 2010. Google Scholar
  24. Thomas Ma, Vijay Menon, and Kate Larson. Improving welfare in one-sided matchings using simple threshold queries. In IJCAI, pages 321-327. ijcai.org, 2021. Google Scholar
  25. David F. Manlove. Algorithmics of Matching Under Preferences, volume 2 of Series on Theoretical Computer Science. WorldScientific, 2013. URL: https://doi.org/10.1142/8591.
  26. N. Megow, J. Meißner, and M. Skutella. Randomization helps computing a minimum spanning tree under uncertainty. SIAM Journal on Computing, 46(4):1217-1240, 2017. URL: https://doi.org/10.1137/16M1088375.
  27. Cheng Ng and Daniel S. Hirschberg. Lower bounds for the stable marriage problem and its variants. SIAM J. Comput., 19(1):71-77, 1990. URL: https://doi.org/10.1137/0219004.
  28. Jannik Peters. Online elicitation of necessarily optimal matchings. In AAAI, pages 5164-5172. AAAI Press, 2022. Google Scholar
  29. Baharak Rastegari, Anne Condon, Nicole Immorlica, Robert W. Irving, and Kevin Leyton-Brown. Reasoning about optimal stable matchings under partial information. In EC, pages 431-448. ACM, 2014. Google Scholar
  30. Baharak Rastegari, Anne Condon, Nicole Immorlica, and Kevin Leyton-Brown. Two-sided matching with partial information. In EC, pages 733-750. ACM, 2013. Google Scholar
  31. Alvin E. Roth and Marilda A. Oliveira Sotomayor. Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis. Econometric Society Monographs. Cambridge University Press, 1990. URL: https://doi.org/10.1017/CCOL052139015X.
  32. Andrew Chi-Chih Yao. Probabilistic computations: Toward a unified measure of complexity. In FOCS, pages 222-227. IEEE Computer Society, 1977. Google Scholar
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