Improved competitive ratios for submodular secretary problems (extended abstract)

Moran Feldman, Joseph Naor, Roy Schwartz

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

Abstract

The Classical Secretary Problem was introduced during the 60's of the 20th century, nobody is sure exactly when. Since its introduction, many variants of the problem have been proposed and researched. In the classical secretary problem, and many of its variant, the input (which is a set of secretaries, or elements) arrives in a random order. In this paper we apply to the secretary problem a simple observation which states that the random order of the input can be generated by independently choosing a random continuous arrival time for each secretary. Surprisingly, this simple observation enables us to improve the competitive ratio of several known and studied variants of the secretary problem. In addition, in some cases the proofs we provide assuming random arrival times are shorter and simpler in comparison to existing proofs. In this work we consider three variants of the secretary problem, all of which have the same objective of maximizing the value of the chosen set of secretaries given a monotone submodular function f. In the first variant we are allowed to hire a set of secretaries only if it is an independent set of a given partition matroid. The second variant allows us to choose any set of up to k secretaries. In the last and third variant, we can hire any set of secretaries satisfying a given knapsack constraint.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings
Pages218-229
Number of pages12
DOIs
StatePublished - 2011
Externally publishedYes
Event14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011 - Princeton, NJ, United States
Duration: 17 Aug 201119 Aug 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6845 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011
Country/TerritoryUnited States
CityPrinceton, NJ
Period17/08/1119/08/11

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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