Stochastic Probing with Increasing Precision

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-01-08 DOI:10.1137/22m149466x

Martin Hoefer, Kevin Schewior, Daniel Schmand

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 148-169, March 2024.
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 [math]-quantile of the underlying distribution of some constant [math]. 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.

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精度不断提高的随机探测

SIAM 离散数学杂志》，第 38 卷，第 1 期，第 148-169 页，2024 年 3 月。摘要。我们考虑一个随机探测的选择问题。有一组项目，其值从独立的分布中抽取。这些分布是事先已知的。每个项目都可以重复测试。每次测试都会减少其值实现的不确定性。我们研究一个测试模型，其中第一次测试揭示了实现值是小于还是大于某个常数[math]的基础分布的[math]-四分位数。随后的测试允许我们进一步缩小实现值所在的区间。可能的测试数量有限，我们的目标是设计接近最优的测试策略，使我们能够最大化所选项目的期望值。我们研究了相同分布和非相同分布，并开发了在这两种情况下都具有恒定近似因子的多项式时间算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.