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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 = f(x) in one variable, we consider the problem of computing the single-peaked (unimodal) curve y =φ(x) minimizing the L2-distance between them. If the input function f is a histogram with O(n) steps or a piecewise linear function with O(n) linear pieces, we design algorithms for computing φ in linear time. We also give an algorithm to(More)
Given a function y 1⁄4 f ðxÞ defined on an interval I 1⁄4 1⁄20; 1 , we consider the problem of approximating f by a kpeaked function y 1⁄4 ðxÞ. Here, a function is k-peaked if the function has at most k maximal peaks (each peak may be a flat interval). If the distance between input function f and output is minimized, we call the optimal k-peaked(More)
We give a unified view to greedy geometric routing algorithms in ad hoc networks. For this, we first present a general form of greedy routing algorithm using a class of objective functions which are invariant under congruent transformations of a point set. We show that several known greedy routing algorithms such as Greedy Routing, Compass Routing, and(More)