Online uniformly inserting points on 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:
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Year:
2010

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Abstract

In this paper, we consider the problem of inserting points in a square grid, which has many background applications, including halftone in reprographic and image processing. We consider an online version of this problem, i.e., the points are inserted one at a time. The objective is to distribute the points as uniformly as possible. Precisely speaking, after each insertion, the gap ratio should be as small as possible. In this paper, we give an insertion strategy with a maximal gap ratio no more than 2√2 ≈ 2.828, which is the first result on uniformly inserting point in a grid. Moreover, we show that no online algorithm can achieve the maximal gap ratio strictly less than 2.5 for a 3 × 3 grid.