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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)
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 [5] 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)