Stochastic Probing with Increasing Precision

Martin Hoefer, Kevin Schewior, Daniel Schmand

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Abstract

We consider a selection problem with stochastic probing. There is a set of items whose values are drawn from independent distributions. The distributions are known in advance. Each item can be tested repeatedly. Each test reduces the uncertainty about the realization of its value. We study a testing model, where the first test reveals whether the realized value is smaller or larger than the c-quantile of the underlying distribution of some constant c \in (0, 1). Subsequent tests allow us to further narrow down the interval in which the realization is located. There is a limited number of possible tests, and our goal is to design near-optimal testing strategies that allow us to maximize the expected value of the chosen item. We study both identical and nonidentical distributions and develop polynomial-time algorithms with constant approximation factors in both scenarios.

OriginalsprogEngelsk
TidsskriftSIAM Journal on Discrete Mathematics
Vol/bind38
Udgave nummer1
Sider (fra-til)148-169
ISSN0895-4801
DOI
StatusUdgivet - 2024

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