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Documents authored by Grammel, Nathaniel

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.23
Approximating Two-Stage Stochastic Supplier Problems

Authors: Brian Brubach, Nathaniel Grammel, David G. Harris, Aravind Srinivasan, Leonidas Tsepenekas, and Anil Vullikanti

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
The main focus of this paper is radius-based (supplier) clustering in the two-stage stochastic setting with recourse, where the inherent stochasticity of the model comes in the form of a budget constraint. We also explore a number of variants where additional constraints are imposed on the first-stage decisions, specifically matroid and multi-knapsack constraints. Our eventual goal is to provide results for supplier problems in the most general distributional setting, where there is only black-box access to the underlying distribution. To that end, we follow a two-step approach. First, we develop algorithms for a restricted version of each problem, in which all possible scenarios are explicitly provided; second, we employ a novel scenario-discarding variant of the standard Sample Average Approximation (SAA) method, in which we crucially exploit properties of the restricted-case algorithms. We finally note that the scenario-discarding modification to the SAA method is necessary in order to optimize over the radius.
Cite as

Brian Brubach, Nathaniel Grammel, David G. Harris, Aravind Srinivasan, Leonidas Tsepenekas, and Anil Vullikanti. Approximating Two-Stage Stochastic Supplier Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{brubach_et_al:LIPIcs.APPROX/RANDOM.2021.23,
  author =	{Brubach, Brian and Grammel, Nathaniel and Harris, David G. and Srinivasan, Aravind and Tsepenekas, Leonidas and Vullikanti, Anil},
  title =	{{Approximating Two-Stage Stochastic Supplier Problems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{23:1--23:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.23},
  URN =		{urn:nbn:de:0030-drops-147163},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.23},
  annote =	{Keywords: Approximation Algorithms, Stochastic Optimization, Two-Stage Recourse Model, Clustering Problems, Knapsack Supplier}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.36
The Stochastic Score Classification Problem

Authors: Dimitrios Gkenosis, Nathaniel Grammel, Lisa Hellerstein, and Devorah Kletenik

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
Consider the following Stochastic Score Classification Problem. A doctor is assessing a patient's risk of developing a certain disease, and can perform n tests on the patient. Each test has a binary outcome, positive or negative. A positive result is an indication of risk, and a patient's score is the total number of positive test results. Test results are accurate. The doctor needs to classify the patient into one of B risk classes, depending on the score (e.g., LOW, MEDIUM, and HIGH risk). Each of these classes corresponds to a contiguous range of scores. Test i has probability p_i of being positive, and it costs c_i to perform. To reduce costs, instead of performing all tests, the doctor will perform them sequentially and stop testing when it is possible to determine the patient's risk category. The problem is to determine the order in which the doctor should perform the tests, so as to minimize expected testing cost. We provide approximation algorithms for adaptive and non-adaptive versions of this problem, and pose a number of open questions.
Cite as

Dimitrios Gkenosis, Nathaniel Grammel, Lisa Hellerstein, and Devorah Kletenik. The Stochastic Score Classification Problem. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{gkenosis_et_al:LIPIcs.ESA.2018.36,
  author =	{Gkenosis, Dimitrios and Grammel, Nathaniel and Hellerstein, Lisa and Kletenik, Devorah},
  title =	{{The Stochastic Score Classification Problem}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{36:1--36:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.36},
  URN =		{urn:nbn:de:0030-drops-94990},
  doi =		{10.4230/LIPIcs.ESA.2018.36},
  annote =	{Keywords: approximation algorithms, symmetric Boolean functions, stochastic probing, sequential testing, adaptivity}
}
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