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Optimal Skeleton Huffman Trees Revisited

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Computer Science – Theory and Applications (CSR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12159))

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Abstract

A skeleton Huffman tree is a Huffman tree in which all disjoint maximal perfect subtrees are shrunk into leaves. Skeleton Huffman trees, besides saving storage space, are also used for faster decoding and for speeding up Huffman-shaped wavelet trees. In 2017 Klein et al. introduced an optimal skeleton tree: for given symbol frequencies, it has the least number of nodes among all optimal prefix-free code trees (not necessarily Huffman’s) with shrunk perfect subtrees. Klein et al. described a simple algorithm that, for fixed codeword lengths, finds a skeleton tree with the least number of nodes; with this algorithm one can process each set of optimal codeword lengths to find an optimal skeleton tree. However, there are exponentially many such sets in the worst case. We describe an \(\mathcal {O}(n^2\log n)\)-time algorithm that, given n symbol frequencies, constructs an optimal skeleton tree and its corresponding optimal code.

Supported by the Russian Science Foundation (RSF), project 18-71-00002.

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Notes

  1. 1.

    If not supported, it can be implemented using a precomputed table of size \(\mathcal {O}(n)\) [6].

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Authors and Affiliations

  1. Ural Federal University, Ekaterinburg, Russia

    Dmitry Kosolobov & Oleg Merkurev

Authors
  1. Dmitry Kosolobov
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  2. Oleg Merkurev
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Correspondence to Dmitry Kosolobov .

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Editors and Affiliations

  1. University of Trier, Trier, Germany

    Henning Fernau

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Kosolobov, D., Merkurev, O. (2020). Optimal Skeleton Huffman Trees Revisited. In: Fernau, H. (eds) Computer Science – Theory and Applications. CSR 2020. Lecture Notes in Computer Science(), vol 12159. Springer, Cham. https://doi.org/10.1007/978-3-030-50026-9_20

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  • DOI: https://doi.org/10.1007/978-3-030-50026-9_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-50025-2

  • Online ISBN: 978-3-030-50026-9

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