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| Title: | Matrix Rounding under the L_p-Discrepancy Measure and Its Application to Digital Halftoning |
| Authors: | Asano, Tetsuo
Katoh, Naoki
Obokata, Koji
Tokuyama, Takeshi |
| Keywords: | approximation algorithm
digital halftoning
discrepancy
linear programming
matrix rounding
network flow
totally unimodular |
| Issue Date: | 2003 |
| Publisher: | Society for Industrial and Applied Mathematics (SIAM) |
| Magazine name: | SIAM Journal on Computing |
| Volume: | 32 |
| Number: | 6 |
| Start page: | 1423 |
| End page: | 1435 |
| DOI: | 10.1137/S0097539702417511 |
| Abstract: | We study the problem of rounding a real-valued matrix into an integer-valued matrix to minimize an L_p-discrepancy measure between them. To define the L_p-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 F. 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 L_p discrepancy. We propose “laminar family” for constructing a practical and well-solvable class of F. Indeed, we show that the problem is solvable in polynomial time if F is the union of two laminar families. Finally, we show that the matrix rounding using L_1 discrepancy for the union of two laminar families is suitable for developing a high-quality digital-halftoning software. |
| Rights: | Copyright (C) 2003 Society for Industrial and Applied Mathematics (SIAM). Tetsuo Asano, Naoki Katoh, Koji Obokata, and Takeshi Tokuyama, SIAM Journal on Computing, 32(6), 2003, 1423-1435. |
| URI: | https://hdl.handle.net/10119/4906 |
| Material Type: | publisher |
| Appears in Collections: | b10-1. 雑誌掲載論文 (Journal Articles)
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| B3022.pdf | | 585Kb | Adobe PDF | View/Open |
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