A knapsack secretary problem with applications

Moshe Babaioff*, Nicole Immorlica, David Kempe, Robert Kleinberg

*Corresponding author for this work

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

142 Scopus citations

Abstract

We consider situations in which a decision-maker with a fixed budget faces a sequence of options, each with a cost and a value, and must select a subset of them online so as to maximize the total value. Such situations arise in many contexts, e.g., hiring workers, scheduling jobs, and bidding in sponsored search auctions. This problem, often called the online knapsack problem, is known to be inapproximable. Therefore, wo make the enabling assumption that elements arrive in a random order. Hence our problem can be thought of as a weighted version of the classical secretary problem, which we call the knapsack secretary problem. Using the random-order assumption, we design a constant-competitive algorithm for arbitrary weights and values, as well as a e-competitive algorithm for the special case when all weights are equal (i.e., the multiple-choice secretary problem). In contrast to previous work on online knapsack problems, we do not assume any knowledge regarding the distribution of weights and values beyond the fact that the order is random.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings
PublisherSpringer Verlag
Pages16-28
Number of pages13
ISBN (Print)9783540742074
DOIs
StatePublished - 2007
Externally publishedYes
Event10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007 - Princeton, NJ, United States
Duration: 20 Aug 200722 Aug 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4627 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007
Country/TerritoryUnited States
CityPrinceton, NJ
Period20/08/0722/08/07

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