{"title":"Simple Algorithms for Stochastic Score Classification with Small Approximation Ratios","authors":"Benedikt M. Plank, Kevin Schewior","doi":"10.1137/22m1523492","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2069-2088, September 2024. <br/> Abstract. We revisit the Stochastic Score Classification (SSC) problem introduced by Gkenosis et al. (ESA 2018): We are given [math] tests. Each test [math] can be conducted at cost [math], and it succeeds independently with probability [math]. Further, a partition of the (integer) interval [math] into [math] smaller intervals is known. The goal is to conduct tests so as to determine that interval from the partition in which the number of successful tests lies while minimizing the expected cost. Ghuge, Gupta, and Nagarajan (IPCO 2022) recently showed that a polynomial-time constant-factor approximation algorithm exists. We show that interweaving the two strategies that order tests increasingly by their [math] and [math] ratios, respectively—as already proposed by Gkensosis et al. for a special case—yields a small approximation ratio. We also show that the approximation ratio can be slightly decreased from 6 to [math] by adding in a third strategy that simply orders tests increasingly by their costs. The similar analyses for both algorithms are nontrivial but arguably clean. Finally, we complement the implied upper bound of [math] on the adaptivity gap with a lower bound of 3/2. Since the lower-bound instance is a so-called unit-cost [math]-of-[math] instance, we settle the adaptivity gap in this case.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"24 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m1523492","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2069-2088, September 2024. Abstract. We revisit the Stochastic Score Classification (SSC) problem introduced by Gkenosis et al. (ESA 2018): We are given [math] tests. Each test [math] can be conducted at cost [math], and it succeeds independently with probability [math]. Further, a partition of the (integer) interval [math] into [math] smaller intervals is known. The goal is to conduct tests so as to determine that interval from the partition in which the number of successful tests lies while minimizing the expected cost. Ghuge, Gupta, and Nagarajan (IPCO 2022) recently showed that a polynomial-time constant-factor approximation algorithm exists. We show that interweaving the two strategies that order tests increasingly by their [math] and [math] ratios, respectively—as already proposed by Gkensosis et al. for a special case—yields a small approximation ratio. We also show that the approximation ratio can be slightly decreased from 6 to [math] by adding in a third strategy that simply orders tests increasingly by their costs. The similar analyses for both algorithms are nontrivial but arguably clean. Finally, we complement the implied upper bound of [math] on the adaptivity gap with a lower bound of 3/2. Since the lower-bound instance is a so-called unit-cost [math]-of-[math] instance, we settle the adaptivity gap in this case.
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.