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Minimax Trees in Linear Time with Applications

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Combinatorial Algorithms (IWOCA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5874))

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Abstract

A minimax tree is similar to a Huffman tree except that, instead of minimizing the weighted average of the leaves’ depths, it minimizes the maximum of any leaf’s weight plus its depth. Golumbic (1976) introduced minimax trees and gave a Huffman-like, \(\mathcal{O}{n \log n}\)-time algorithm for building them. Drmota and Szpankowski (2002) gave another \(\mathcal{O}{n \log n}\)-time algorithm, which takes linear time when the weights are already sorted by their fractional parts. In this paper we give the first linear-time algorithm for building minimax trees for unsorted real weights.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Wroclaw, Poland

    Paweł Gawrychowski

  2. Research Group in Genome Informatics, Bielefeld University, Germany

    Travis Gagie

Authors
  1. Paweł Gawrychowski
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  2. Travis Gagie
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Editor information

Editors and Affiliations

  1. Institute for Theoretical Computer Science and Department of Applied Mathematics, Charles University, Prague, Czech Republic

    Jiří Fiala  & Jan Kratochvíl  & 

  2. School of Electrical Engineering and Computer Science, The University of Newcastle, University Drive, NSW 2308, Callaghan, Australia

    Mirka Miller

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© 2009 Springer-Verlag Berlin Heidelberg

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Gawrychowski, P., Gagie, T. (2009). Minimax Trees in Linear Time with Applications. In: Fiala, J., Kratochvíl, J., Miller, M. (eds) Combinatorial Algorithms. IWOCA 2009. Lecture Notes in Computer Science, vol 5874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10217-2_28

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  • DOI: https://doi.org/10.1007/978-3-642-10217-2_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10216-5

  • Online ISBN: 978-3-642-10217-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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