TY - JOUR

T1 - Stable Secretaries

AU - Babichenko, Yakov

AU - Emek, Yuval

AU - Feldman, Michal

AU - Patt-Shamir, Boaz

AU - Peretz, Ron

AU - Smorodinsky, Rann

N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2019/8/1

Y1 - 2019/8/1

N2 - 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.

AB - 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.

KW - Assignment problem

KW - Secretary problem

KW - Stable matching

UR - http://www.scopus.com/inward/record.url?scp=85064662463&partnerID=8YFLogxK

U2 - 10.1007/s00453-019-00569-6

DO - 10.1007/s00453-019-00569-6

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AN - SCOPUS:85064662463

SN - 0178-4617

VL - 81

SP - 3136

EP - 3161

JO - Algorithmica

JF - Algorithmica

IS - 8

ER -