Matrix rounding under the Lp-discrepancy measure and its application to digital halftoning

Tetsuo Asano, Naoki Katoh, Koji Obokata, Takeshi Tokuyama

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

18 Citations (Scopus)

Abstract

In this paper we study the problem of rounding a real-valued matrix into an integer-valued matrix to rmmmize an Lp-discrepancy measure between them. To define the Lp-discrepancy measure, we introduce a family F of regions (rigid submatrices) of the matrix, and consider a hypergraph defined by the family. The difficulty of the problem depends on the choice of the region family J-. We first investigate the rounding problem by using integer programming problems with convex piecewise-linear objective functions, and give some nontrivial upper bounds for the Lp-discrepancy. Then, we propose "laminar family" for constructing a practical and well-solvable class of T. Indeed, we show that the problem is solvable in polynomial time if T is a union of two laminar families. Finally, we show that the matrix rounding using Li-discrepancy for a union of two laminar families is suitable for developing a high-quality digital-halftoning software.

Original languageEnglish
Title of host publicationProceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002
PublisherAssociation for Computing Machinery
Pages896-904
Number of pages9
ISBN (Electronic)089871513X
Publication statusPublished - 2002 Jan 1
Event13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002 - San Francisco, United States
Duration: 2002 Jan 62002 Jan 8

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume06-08-January-2002

Other

Other13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002
CountryUnited States
CitySan Francisco
Period02/1/602/1/8

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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