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Algorithmica

pp 1–26 | Cite as

Stable Secretaries

  • Yakov Babichenko
  • Yuval Emek
  • Michal Feldman
  • Boaz Patt-ShamirEmail author
  • Ron Peretz
  • Rann Smorodinsky
Article
  • 25 Downloads

Abstract

In the classical secretary problem, multiple secretaries arrive one at a time to compete for a single position, and the goal is to choose the best secretary to the job while knowing the candidate’s quality only with respect to the preceding candidates. In this paper we define and study a new variant of the secretary problem, in which there are multiple jobs. The applicants are ranked relatively upon arrival as usual, and, in addition, we assume that the jobs are also ranked. The main conceptual novelty in our model is that we evaluate a matching using the notion of blocking pairs from Gale and Shapley’s stable matching theory. Specifically, our goal is to maximize the number of matched jobs (or applicants) that do not take part in a blocking pair. We study the cases where applicants arrive randomly or in adversarial order, and provide upper and lower bounds on the quality of the possible assignment assuming all jobs and applicants are totally ordered. Among other results, we show that when arrival is uniformly random, a constant fraction of the jobs can be satisfied in expectation, or a constant fraction of the applicants, but not a constant fraction of the matched pairs.

Keywords

Secretary problem Stable matching Assignment problem 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Yakov Babichenko
    • 1
  • Yuval Emek
    • 1
  • Michal Feldman
    • 2
  • Boaz Patt-Shamir
    • 2
    Email author
  • Ron Peretz
    • 3
  • Rann Smorodinsky
    • 1
  1. 1.TechnionHaifaIsrael
  2. 2.Tel Aviv UniversityTel AvivIsrael
  3. 3.Bar Ilan UniversityRamat GanIsrael

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