Approximation Algorithms for Optimal Decision Trees and Adaptive TSP Problems

  • Anupam Gupta
  • Viswanath Nagarajan
  • R. Ravi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6198)

Abstract

We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of m possible diseases, each test having a cost, and the a-priori likelihood of the patient having any particular disease, what is a good adaptive strategy to perform these tests to minimize the expected cost to identify the disease? We settle the approximability of this problem by giving a tight O(logm)-approximation algorithm.

We also consider a more substantial generalization, the Adaptive TSP problem, which can be used to model switching costs between tests in the optimal decision tree problem. Given an underlying metric space, a random subset S of cities is drawn from a known distribution, but S is initially unknown to us—we get information about whether any city is in S only when we visit the city in question. What is a good adaptive way of visiting all the cities in the random subset S while minimizing the expected distance traveled? For this adaptive TSP problem, we give the first poly-logarithmic approximation, and show that this algorithm is best possible unless we can improve the approximation guarantees for the well-known group Steiner tree problem.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Anupam Gupta
    • 1
  • Viswanath Nagarajan
    • 2
  • R. Ravi
    • 3
  1. 1.Computer Science DepartmentCarnegie Mellon UniversityPittsburghUSA
  2. 2.IBM T.J. Watson Research CenterUSA
  3. 3.Tepper School of BusinessCarnegie Mellon UniversityPittsburghUSA

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