Minimax Trees in Linear Time with Applications

  • Authors:

  • Paweł Gawrychowski;Travis Gagie

  • Affiliations:

  • Institute of Computer Science, University of Wroclaw, Poland;Research Group in Genome Informatics, Bielefeld University, Germany

  • Venue:
  • Combinatorial Algorithms
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

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.