A framework for the secretary problem on the intersection of matroids

Moran Feldman, Ola Svensson, Rico Zenklusen

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The secretary problem became one of the most prominent online selection problems due to its numerous applications in online mechanism design. The task is to select a maximum weight subset of elements subject to given constraints, where elements arrive one-by-one in random order, revealing a weight upon arrival. The decision whether to select an element has to be taken immediately after its arrival. The different applications that map to the secretary problem ask for different constraint families to be handled. The most prominent ones are matroid constraints, which both capture many relevant settings and admit strongly competitive secretary algorithms. However, dealing with more involved constraints proved to be much more difficult, and strong algorithms are known only for a few specific settings. In this paper, we present a general framework for dealing with the secretary problem over the intersection of several matroids. This framework allows us to combine and exploit the large set of matroid secretary algorithms known in the literature. As one consequence, we get constant-competitive secretary algorithms over the intersection of any constant number of matroids whose corresponding (single-)matroid secretary problems are currently known to have a constant-competitive algorithm. Moreover, we show that our results extend to submodular objectives.

Original languageEnglish
Title of host publication29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
EditorsArtur Czumaj
PublisherAssociation for Computing Machinery
Pages735-752
Number of pages18
ISBN (Electronic)9781611975031
DOIs
StatePublished - 2018
Externally publishedYes
Event29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, United States
Duration: 7 Jan 201810 Jan 2018

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
Country/TerritoryUnited States
CityNew Orleans
Period7/01/1810/01/18

Bibliographical note

Funding Information:
∗SupportedbyIsraelScienceFoundation grant1357/16,ERC Starting Grant 335288-OptAppro x, and Swiss National Science Foundation grant200021 165866. †Dept. ofMathematicsandComputerScience, OpenUniversity of Israel. Email: moranfe@openu.ac.il. ‡SchoolofComputerandCommunication Sciences, EPFL. Email:ola.svensson@epfl.ch. §DepartmentofMathematics, ETHZurich, Zurich, Switzerland. Email: ricoz@math.ethz.ch.

Publisher Copyright:
© Copyright 2018 by SIAM.

Keywords

  • Matroid intersection
  • Matroid secretary problem
  • Online algorithms

ASJC Scopus subject areas

  • Software
  • Mathematics (all)

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