### 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.

Original language | English (US) |
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Title of host publication | 26th European Symposium on Algorithms, ESA 2018 |

Editors | Hannah Bast, Grzegorz Herman, Yossi Azar |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Print) | 9783959770811 |

DOIs | |

State | Published - Aug 1 2018 |

Event | 26th European Symposium on Algorithms, ESA 2018 - Helsinki, Finland Duration: Aug 20 2018 → Aug 22 2018 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 112 |

ISSN (Print) | 1868-8969 |

### Other

Other | 26th European Symposium on Algorithms, ESA 2018 |
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Country | Finland |

City | Helsinki |

Period | 8/20/18 → 8/22/18 |

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### Keywords

- Adaptivity
- Approximation algorithms
- Sequential testing
- Stochastic probing
- Symmetric boolean functions

### ASJC Scopus subject areas

- Software

### Cite this

*26th European Symposium on Algorithms, ESA 2018*(Leibniz International Proceedings in Informatics, LIPIcs; Vol. 112). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ESA.2018.36