David M. Mount

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Consider a set of <italic>S</italic> of <italic>n</italic> data points in real <italic>d</italic>-dimensional space, R<supscrpt>d</supscrpt>, where distances are measured using any Minkowski metric. In nearest neighbor searching, we preprocess <italic>S</italic> into a data structure, so that given any query point <italic>q</italic><inline-equation>(More)
ÐIn k-means clustering, we are given a set of n data points in d-dimensional space R and an integer k and the problem is to determine a set of k points in R, called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k-means clustering is Lloyd's algorithm. In this paper, we present a(More)
We present an algorithm for determining the shortest path between a source and a destination on an arbitrary (possibly nonconvex) polyhedral surface. The path is constrained to lie on the surface, and distances are measured according to the Euclidean metric. Our algorithm runs in time O(n log n) and requires O(n2) space, where n is the number of edges of(More)
Let S denote a set of n points in d-dimensional space, Rd, and let dist(p, g) denote the distance between two points in any Minkowski metric. For any real E > 0 and q E Rd, a point p E S is a (1 + c)-approximate nearest neighbor of q if, for all p’ E S, we have dist(p, q)/dist(p’,q) 5 (1 + E). We show how to preprocess a set of n points in Rd in O(nlog n)(More)
Euclidean spanners are important data structures in geometric algorithm design, because they provide a means of approximating the complete Euclidean graph with only O(n) edges, so that the shortest path length between each pair of points is not more than a constant factor longer than the Euclidean distance between the points. In many applications of(More)
In <i>k</i>-means clustering we are given a set of <i>n</i> data points in <i>d</i>-dimensional space R<sup>d</sup> and an integer <i>k</i>, and the problem is to determine a set of <i>k</i> points in &#211C;<sup>d</sup>, called <i>centers</i>, to minimize the mean squared distance from each data point to its nearest center. No exact polynomial-time(More)
Facility location problems are traditionally investigated with the assumption that <i>all</i> the clients are to be provided service. A significant shortcoming of this formulation is that a few very distant clients, called <i>outliers</i>, can exert a disproportionately strong influence over the final solution. In this paper we explore a generalization of(More)
The range searching problem is a fundamental problem in computational geometry, with numerous important applications. Most research has focused on solving this problem exactly, but lower bounds show that if linear space is assumed, the problem cannot be solved in polylogarithmic time, except for the case of orthogonal ranges. In this paper we show that if(More)