Stable Secretaries

Yakov Babichenko; Yuval Emek; Michal Feldman; Boaz Patt-Shamir; Ron Peretz; Rann Smorodinsky

doi:10.1007/s00453-019-00569-6

Stable Secretaries

Yakov Babichenko, Yuval Emek, Michal Feldman, Boaz Patt-Shamir, Ron Peretz, Rann Smorodinsky

Department of Economics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	3136-3161
Number of pages	26
Journal	Algorithmica
Volume	81
Issue number	8
DOIs	https://doi.org/10.1007/s00453-019-00569-6
State	Published - 1 Aug 2019

Bibliographical note

Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Funding

Y. Babichenko was supported by the Israel Science Foundation Grant Number 2021296. The work of Y. Emek was supported in part by an Israeli Science Foundation Grant Number 1016/17 and by grants from the Bernard M. Gordon Center for Systems Engineering and the Center for Security Science and Technology at the Technion. The work of M. Feldman was partially supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement number 337122. The work of B. Patt-Shamir was supported in part by the Israel Science Foundation Grant Number 1444/14. R. Smorodinsky was supported by GIF research Grant No. I-1419-118.4/2017, Technion VPR grants, the Bernard M. Gordon Center for Systems Engineering at the Technion, and the TASP Center at the Technion.

Funders	Funder number
Bernard M. Gordon Center for Systems Engineering
Center for Security Science and Technology
FP7/2007
Israeli Science Foundation	1016/17
European Commission	337122, 1444/14
German-Israeli Foundation for Scientific Research and Development	I-1419-118.4/2017
Israel Science Foundation	2021296
Seventh Framework Programme
Technion-Israel Institute of Technology

Keywords

Assignment problem
Secretary problem
Stable matching

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10.1007/s00453-019-00569-6

Cite this

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Stable Secretaries

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Keywords

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