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An Approximation Algorithm for Binary Searching in Trees

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Abstract

We consider the problem of computing efficient strategies for searching in trees. As a generalization of the classical binary search for ordered lists, suppose one wishes to find a (unknown) specific node of a tree by asking queries to its arcs, where each query indicates the endpoint closer to the desired node. Given the likelihood of each node being the one searched, the objective is to compute a search strategy that minimizes the expected number of queries. Practical applications of this problem include file system synchronization and software testing. Here we present a linear time algorithm which is the first constant factor approximation for this problem. This represents a significant improvement over previous O(log n)-approximation.

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Authors and Affiliations

  1. Informatics Department, PUC-Rio, Rua Marquês de São Vicente 225, RDC, 4º andar, CEP 22453-900, Rio de Janeiro, RJ, Brazil

    Eduardo Laber

  2. Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA

    Marco Molinaro

Authors
  1. Eduardo Laber
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  2. Marco Molinaro
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Corresponding author

Correspondence to Marco Molinaro.

Additional information

Preliminary version of this paper appeared in ICALP 2008.

The first author was partially supported by CNPq (Proc. 304786/2006-3 and 470654/2007-4), and by FAPERJ (Proj. E-26/100.505/2007).

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Laber, E., Molinaro, M. An Approximation Algorithm for Binary Searching in Trees. Algorithmica 59, 601–620 (2011). https://doi.org/10.1007/s00453-009-9325-0

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  • DOI: https://doi.org/10.1007/s00453-009-9325-0

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