research-article

Matroid Secretary Problems

Authors:

Moshe Babaioff,

Nicole Immorlica,

Robert KleinbergAuthors Info & Claims

Journal of the ACM (JACM), Volume 65, Issue 6

Article No.: 35, Pages 1 - 26

https://doi.org/10.1145/3212512

Published: 19 November 2018 Publication History

Abstract

We define a generalization of the classical secretary problem called the matroid secretary problem. In this problem, the elements of a matroid are presented to an online algorithm in uniformly random order. When an element arrives, the algorithm observes its value and must make an irrevocable decision whether or not to accept it. The accepted elements must form an independent set, and the objective is to maximize the combined value of these elements. We present an O(log k)-competitive algorithm for general matroids (where k is the rank of the matroid), and constant-competitive algorithms for several special cases including graphic matroids, truncated partition matroids, and bounded degree transversal matroids. We leave as an open question the existence of constant-competitive algorithms for general matroids. Our results have applications in welfare-maximizing online mechanism design for domains in which the sets of simultaneously satisfiable agents form a matroid.

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Cited By

Correa JCristi AEpstein BSoto J(2024)Sample-Driven Optimal StoppingMathematics of Operations Research10.1287/moor.2023.136349:1(441-475)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1287/moor.2023.1363
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
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Published In

cover image Journal of the ACM

Journal of the ACM Volume 65, Issue 6

December 2018

331 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/3293435

Editor:
Éva Tardos
Cornell University

Issue’s Table of Contents

Copyright © 2018 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 19 November 2018

Accepted: 01 April 2018

Revised: 01 April 2018

Received: 01 November 2016

Published in JACM Volume 65, Issue 6

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Cited By

Correa JCristi AEpstein BSoto J(2024)Sample-Driven Optimal StoppingMathematics of Operations Research10.1287/moor.2023.136349:1(441-475)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1287/moor.2023.1363
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
Gravin NSun ETang Z(2023)Online Ordinal Problems: Optimality of Comparison-based Algorithms and their Cardinal Complexity2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00113(1863-1876)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00113
Antoniadis AGouleakis TKleer PKolev P(2023)Secretary and online matching problems with machine learned adviceDiscrete Optimization10.1016/j.disopt.2023.10077848(100778)Online publication date: May-2023
https://doi.org/10.1016/j.disopt.2023.100778
Santiago RSergeev IZenklusen R(2023)Constant-Competitiveness for Random Assignment Matroid Secretary Without Knowing the MatroidInteger Programming and Combinatorial Optimization10.1007/978-3-031-32726-1_30(423-437)Online publication date: 21-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-32726-1_30
Ezra TFeldman MGravin NTang ZPennock DSegal ISeuken S(2022)General Graphs are Easier than Bipartite Graphs: Tight Bounds for Secretary MatchingProceedings of the 23rd ACM Conference on Economics and Computation10.1145/3490486.3538290(1148-1177)Online publication date: 12-Jul-2022
https://dl.acm.org/doi/10.1145/3490486.3538290
Albers SGálvez WJanke M(2022)Machine Covering in the Random-Order ModelAlgorithmica10.1007/s00453-022-01011-085:6(1560-1585)Online publication date: 23-Jul-2022
https://dl.acm.org/doi/10.1007/s00453-022-01011-0
Abels ALadewig LSchewior KStinzendörfer M(2022)Knapsack Secretary Through BoostingApproximation and Online Algorithms10.1007/978-3-031-18367-6_4(61-81)Online publication date: 21-Oct-2022
https://doi.org/10.1007/978-3-031-18367-6_4
Albers SLadewig L(2021)New results for the k-secretary problemTheoretical Computer Science10.1016/j.tcs.2021.02.022Online publication date: Feb-2021
https://doi.org/10.1016/j.tcs.2021.02.022
Kordecki W(2021)Secretary Problem: Graphs, Matroids and GreedoidsOperations Research Forum10.1007/s43069-021-00092-x2:4Online publication date: 17-Nov-2021
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