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

Tetsuo Asano, Naoki Katoh, Koji Obokata, Takeshi Tokuyama

研究成果: Conference contribution

18 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトルProceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002
出版社Association for Computing Machinery
ページ896-904
ページ数9
ISBN(電子版)089871513X
出版ステータスPublished - 2002 1 1
イベント13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002 - San Francisco, United States
継続期間: 2002 1 62002 1 8

出版物シリーズ

名前Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
06-08-January-2002

Other

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

ASJC Scopus subject areas

  • ソフトウェア
  • 数学 (全般)

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