License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/DagSemProc.09281.4
URN: urn:nbn:de:0030-drops-22421
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Gawrychowski, Pawel ; Gagie, Travis

Minimax Trees in Linear Time with Applications

09281.GagieTravis.Paper.2242.pdf (0.2 MB)


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, $O (n log n)$-time algorithm for building them. Drmota and Szpankowski (2002) gave another $O (n log n)$-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.

BibTeX - Entry

  author =	{Gawrychowski, Pawel and Gagie, Travis},
  title =	{{Minimax Trees in Linear Time with Applications}},
  booktitle =	{Search Methodologies},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9281},
  editor =	{Rudolf Ahlswede and Ferdinando Cicalese and Ugo Vaccaro},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-22421},
  doi =		{10.4230/DagSemProc.09281.4},
  annote =	{Keywords: Data structures, data compression, prefix-free coding}

Keywords: Data structures, data compression, prefix-free coding
Collection: 09281 - Search Methodologies
Issue Date: 2009
Date of publication: 10.11.2009

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