IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v70y2022i3p1873-1890.html
   My bibliography  Save this article

Legal Assignments and Fast EADAM with Consent via Classic Theory of Stable Matchings

Author

Listed:
  • Yuri Faenza

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Xuan Zhang

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

Gale and Shapley’s stable assignment problem has been extensively studied, applied, and extended. In the context of school choice, mechanisms often aim at finding an assignment that is more favorable to students. We investigate two extensions introduced in this framework— legal assignments and the efficiency adjusted deferred acceptance mechanism (EADAM) algorithm—through the lens of the classic theory of stable matchings. In any instance, the set L of legal assignments is known to contain all stable assignments. We prove that L is exactly the set of stable assignments in another instance. Moreover, we show that essentially all optimization problems over L can be solved within the same time bound needed for solving it over the set of stable assignments. A key tool for this latter result is an algorithm that finds the student-optimal legal assignment. We then generalize our algorithm to obtain the assignment output of EADAM with any given set of consenting students without sacrificing the running time, hence largely improving in both theory and practice over known algorithms. Finally, we show that the set L can be much larger than the set of stable matchings, connecting legal matchings with certain concepts and open problems in the literature.

Suggested Citation

  • Yuri Faenza & Xuan Zhang, 2022. "Legal Assignments and Fast EADAM with Consent via Classic Theory of Stable Matchings," Operations Research, INFORMS, vol. 70(3), pages 1873-1890, May.
    • Handle: RePEc:inm:oropre:v:70:y:2022:i:3:p:1873-1890
    DOI: 10.1287/opre.2021.2199
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2021.2199
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2021.2199?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:70:y:2022:i:3:p:1873-1890. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.