Uniformly inserting points on square grid

Authors:
Yong Zhang;Zhuo Chang;Francis Y. L. Chin;Hing-Fung Ting;Yung H. Tsin
Affiliations:
College of Mathematics and Computer Science, Hebei University, China and Department of Computer Science, The University of Hong Kong, Hong Kong;College of Mathematics and Computer Science, Hebei University, China;Department of Computer Science, The University of Hong Kong, Hong Kong;Department of Computer Science, The University of Hong Kong, Hong Kong;School of Computer Science, University of Windsor, Canada
Venue:
Information Processing Letters
Year:
2011

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Abstract

We consider the problem of inserting points in a square grid, which has many motivations, including halftoning in reprography and image processing. The points are inserted one at a time. The objective is to distribute the points as uniformly as possible. More specifically, after each insertion, the gap ratio should be as small as possible. We give an insertion strategy with a maximal gap ratio no more than 22~2.828, which is the first result in uniformly inserting points in a grid. Moreover, we show that no online algorithm can achieve the maximal gap ratio strictly less than 2.5 for a 3x3 grid.