Approximation Algorithms for Optimal Decision Trees and Adaptive TSP Problems

  • Anupam Gupta
  • Viswanath Nagarajan
  • R. Ravi
Conference paper

DOI: 10.1007/978-3-642-14165-2_58

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6198)
Cite this paper as:
Gupta A., Nagarajan V., Ravi R. (2010) Approximation Algorithms for Optimal Decision Trees and Adaptive TSP Problems. In: Abramsky S., Gavoille C., Kirchner C., Meyer auf der Heide F., Spirakis P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6198. Springer, Berlin, Heidelberg

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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