Approximation Algorithms for Optimal Decision Trees and Adaptive TSP Problems

摘要

We consider the problem of constructing optimal decision trees: given a collection of tests that can disambiguate between a set of m possible diseases, each test having a cost, and the a priori likelihood of any particular disease, what is a good adaptive strategy to perform these tests to minimize the expected cost to identify the disease? This problem has been studied in several works, with O(log m)-approximations known in the special cases when either costs or probabilities are uniform. In this paper, we settle the approximability of the general problem by giving a tight O(log m)-approximation algorithm.