How to color a checkerboard with a given distribution - Matrix rounding achieving low 2 × 2-discrepancy

Tetsuo Asano, Takeshi Tokuyama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Citations (Scopus)

Abstract

Motivated by a digital halftoning application to convert a continuous-tone image into a binary image, we discusses how to round a [0, 1]-valued matrix into a 0, 1 binary matrix achieving lowdi screpancy with respect to the family of all 2×2 square submatrices (or regions). A trivial upper bound of the discrepancy is 2 and the known lower bound is 1. In this paper we shall show howto achieve a new upper bound 5/3 using a newpro of technique based on modified graph matching.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 12th International Symposium, ISAAC 2001, Proceedings
Pages636-648
Number of pages13
DOIs
Publication statusPublished - 2001 Dec 1
Event12th International Symposium on Algorithms and Computation, ISAAC 2001 - Christchurch, New Zealand
Duration: 2001 Dec 192001 Dec 21

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2223 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other12th International Symposium on Algorithms and Computation, ISAAC 2001
CountryNew Zealand
CityChristchurch
Period01/12/1901/12/21

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Asano, T., & Tokuyama, T. (2001). How to color a checkerboard with a given distribution - Matrix rounding achieving low 2 × 2-discrepancy. In Algorithms and Computation - 12th International Symposium, ISAAC 2001, Proceedings (pp. 636-648). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2223 LNCS). https://doi.org/10.1007/3-540-45678-3_54