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Compressed Tree Representations

  • Living reference work entry
  • First Online:
Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

1989; Jacobson

2001; Munro, Raman

2005; Benoit, Demaine, Munro, Raman, S. Rao

2014; Navarro, Sadakane

Problem Definition

The problem is, given a tree, to encode it compactly so that basic operations on the tree are done quickly, preferably in constant time for static trees. Here, we consider the most basic class of trees: rooted ordered unlabeled trees. The information-theoretic lower bound for representing an n-node ordered tree is 2n − o(n) bits because there are \({2n - 2\choose n - 1}/n\) different trees. Therefore, the aim is to encode an ordered tree in 2n + o(n) bits including auxiliary data structures so that basic operations are done quickly. We assume that the computation model is the Θ(logn)-bit word RAM, that is, memory access for consecutive Θ(logn) bits and arithmetic and logical operations on two Θ(logn)-bit integers are done in constant time.

Preliminaries

Let X be a string on alphabet \(\mathcal{A}\). The number of...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Chile, Santiago, Chile

    Gonzalo Navarro

  2. Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan

    Kunihiko Sadakane

Authors
  1. Gonzalo Navarro
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  2. Kunihiko Sadakane
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Corresponding author

Correspondence to Kunihiko Sadakane .

Editor information

Editors and Affiliations

  1. Dept. Electrical Engineering & Computer Science, Northwestern University, Evanston, Illinois, USA

    Ming-Yang Kao

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Navarro, G., Sadakane, K. (2015). Compressed Tree Representations. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27848-8_641-1

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  • DOI: https://doi.org/10.1007/978-3-642-27848-8_641-1

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  • Online ISBN: 978-3-642-27848-8

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