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Given a fixed origin <i>o</i> in the <i>d</i>-dimensional grid, we give a novel definition of <i>digital rays dig(op)</i> from <i>o</i> to each grid point <i>p</i>. Each digital ray dig(<i>op</i>) approximates the Euclidean line segment <i>op</i> between <i>o</i> and <i>p</i>. The set of all digital rays satisfies a set of axioms analogous to the Euclidean… (More)
Motivated by the work of Asano et al. , we consider the distance trisector problem and zone diagram considering segments in the plane as the input geometric objects. As the most basic case, we first consider the pair of curves (distance trisector curves) trisecting the distance between a point and a line, as shown in Figure 1. This is a natural extension… (More)
We consider the optimization problem of finding k nonintersecting rectangles and tableaux in n × n pixel plane where each pixel has a real valued weight. We discuss existence of efficient algorithms if a corner point of each rectangle/tableau is specified.
Given a function y ¼ f ðxÞ in one variable, we consider the problem of computing a k-peaked curve y ¼ ðxÞ minimizing the L p distance between them. In other words, ðxÞ has at most k local peaks and minimizes the area bounded by the curves f ðxÞ and ðxÞ. This gives extension of the authors' previous work  on the unimodal (i.e., single-peaked)… (More)
The maximum closure problem of a vertex-weighted directed graph is a classical optimization problem. Motivated by image segmentation and data mining applications, we consider a variant that computes the maximum union of closures of two different graphs on a shared vertex set. We show that the problem is NP-hard to approximate within a bounded approximation… (More)