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Approximating Optimal Binary Decision Trees

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Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques (APPROX 2008, RANDOM 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5171))

Abstract

We give a (ln n + 1)-approximation for the decision tree (DT) problem. An instance of DT is a set of m binary tests T = (T 1, ..., T m ) and a set of n items X = (X 1, ..., X n ). The goal is to output a binary tree where each internal node is a test, each leaf is an item and the total external path length of the tree is minimized. Total external path length is the sum of the depths of all the leaves in the tree. DT has a long history in computer science with applications ranging from medical diagnosis to experiment design. It also generalizes the problem of finding optimal average-case search strategies in partially ordered sets which includes several alphabetic tree problems. Our work decreases the previous upper bound on the approximation ratio by a constant factor. We provide a new analysis of the greedy algorithm that uses a simple accounting scheme to spread the cost of a tree among pairs of items split at a particular node. We conclude by showing that our upper bound also holds for the DT problem with weighted tests.

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Authors and Affiliations

  1. Department of Computer Science, University of Massachusetts, Amherst, 140 Governors Drive, Amherst, MA 01003

    Micah Adler

  2. Department of Computer Science, Williams College, 47 Lab Campus Drive, Williamstown, MA 01267

    Brent Heeringa

Authors
  1. Micah Adler
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  2. Brent Heeringa
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Ashish Goel Klaus Jansen José D. P. Rolim Ronitt Rubinfeld

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© 2008 Springer-Verlag Berlin Heidelberg

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Adler, M., Heeringa, B. (2008). Approximating Optimal Binary Decision Trees. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2008 2008. Lecture Notes in Computer Science, vol 5171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85363-3_1

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  • DOI: https://doi.org/10.1007/978-3-540-85363-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85362-6

  • Online ISBN: 978-3-540-85363-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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