How to Color a Checkerboard with a Given Distribution -- Matrix Rounding Achieving Low 2 × 2-Discrepancy

Authors:
Tetsuo Asano;Takeshi Tokuyama
Affiliations:
School of Information Science, Japan Advanced Institute of Science and Technology, Japan;Graduate School of Information Sciences, Tohoku University, Japan
Venue:
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Year:
2009

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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脳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.