  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 test result is an indication of risk, and a patient's score is the
total number of positive test results. 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
the test. To reduce costs, instead of performing all tests, the doctor will
perform them sequentially and stop testing when it is possible to determine the
risk category for the patient. The problem is to determine the order in which
the doctor should perform the tests, so as to minimize the expected testing
cost. We provide approximation algorithms for adaptive and non-adaptive
versions of this problem, and pose a number of open questions.
