Online uniformly inserting points on grid

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. © Springer-Verlag Berlin Heidelberg 2010.link_to_subscribed_fulltextThe 6th International Conference on Algorithmic Aspects in Information and Management (AAIM 2010), Weihai, China, 19-21 June 2010. In Lecture Notes in Computer Science, 2010, v. 6124, p. 281–29