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Beyond matroids: secretary problem and prophet inequality with general constraints

Author:

Aviad RubinsteinAuthors Info & Claims

STOC '16: Proceedings of the forty-eighth annual ACM symposium on Theory of Computing

Pages 324 - 332

https://doi.org/10.1145/2897518.2897540

Published: 19 June 2016 Publication History

Abstract

We study generalizations of the ``Prophet Inequality'' and ``Secretary Problem'', where the algorithm is restricted to an arbitrary downward-closed set system. For 0,1 values, we give O(n)-competitive algorithms for both problems. This is close to the Omega(n/log n) lower bound due to Babaioff, Immorlica, and Kleinberg. For general values, our results translate to O(log(n) log(r))-competitive algorithms, where r is the cardinality of the largest feasible set. This resolves (up to the O(loglog(n) log(r)) factor) an open question posed to us by Bobby Kleinberg.

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M. Babaioff, N. Immorlica, D. Kempe, and R. Kleinberg. Online auctions and generalized secretary problems. SIGecom Exch., 7(2):7:1–7:11, June 2008.

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Cited By

Ezra TFeldman MTang ZKleinberg RSaban DBergemann D(2024)Choosing Behind the Veil: Tight Bounds for Identity-Blind Online AlgorithmsProceedings of the 25th ACM Conference on Economics and Computation10.1145/3670865.3673620(136-158)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3670865.3673620
Ekbatani FNiazadeh RNuti PVondrák JMohar BShinkar IO'Donnell R(2024)Prophet Inequalities with Cancellation CostsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649786(1247-1258)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649786
Kesselheim TMolinaro MSingla SMohar BShinkar IO'Donnell R(2024)Supermodular Approximation of Norms and ApplicationsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649734(1841-1852)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649734
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Index Terms

Beyond matroids: secretary problem and prophet inequality with general constraints
1. Theory of computation
  1. Models of computation

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cover image ACM Conferences

STOC '16: Proceedings of the forty-eighth annual ACM symposium on Theory of Computing

June 2016

1141 pages

ISBN:9781450341325

DOI:10.1145/2897518

General Chair:
Daniel Wichs
Northeastern, USA
,
Program Chair:
Yishay Mansour
Tel Aviv

Copyright © 2016 ACM.

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Published: 19 June 2016

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June 19 - 21, 2016

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Cited By

Ezra TFeldman MTang ZKleinberg RSaban DBergemann D(2024)Choosing Behind the Veil: Tight Bounds for Identity-Blind Online AlgorithmsProceedings of the 25th ACM Conference on Economics and Computation10.1145/3670865.3673620(136-158)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3670865.3673620
Ekbatani FNiazadeh RNuti PVondrák JMohar BShinkar IO'Donnell R(2024)Prophet Inequalities with Cancellation CostsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649786(1247-1258)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649786
Kesselheim TMolinaro MSingla SMohar BShinkar IO'Donnell R(2024)Supermodular Approximation of Norms and ApplicationsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649734(1841-1852)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649734
Chekuri CLivanos V(2024)On submodular prophet inequalities and correlation gapTheoretical Computer Science10.1016/j.tcs.2024.1148141019:COnline publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1016/j.tcs.2024.114814
DeHaan IPashkovich K(2024)Matroid Bayesian Online SelectionAlgorithmic Game Theory10.1007/978-3-031-71033-9_23(405-422)Online publication date: 31-Aug-2024
https://doi.org/10.1007/978-3-031-71033-9_23
Marinkovic JSoto JVerdugo V(2024)Online Combinatorial Assignment in Independence SystemsInteger Programming and Combinatorial Optimization10.1007/978-3-031-59835-7_22(294-308)Online publication date: 22-May-2024
https://doi.org/10.1007/978-3-031-59835-7_22
Immorlica NSingla SWaggoner B(2023)Prophet Inequalities with Linear Correlations and AugmentationsACM Transactions on Economics and Computation10.1145/3623273Online publication date: 8-Sep-2023
https://dl.acm.org/doi/10.1145/3623273
Cai LGardner JWeinberg S(2023)Optimal Stopping with Multi-dimensional Comparative Loss AversionWeb and Internet Economics10.1007/978-3-031-48974-7_6(95-112)Online publication date: 4-Dec-2023
https://dl.acm.org/doi/10.1007/978-3-031-48974-7_6
Ezra TLeonardi SReiffenhäuser RRusso MTsigonias-Dimitriadis A(2023)Prophet Inequalities via the Expected Competitive RatioWeb and Internet Economics10.1007/978-3-031-48974-7_16(272-289)Online publication date: 31-Dec-2023
https://doi.org/10.1007/978-3-031-48974-7_16
Deng YMirrokni VZhang HKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Posted pricing and dynamic prior-independent mechanisms with value maximizersProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3602024(24158-24169)Online publication date: 28-Nov-2022
https://dl.acm.org/doi/10.5555/3600270.3602024
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