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An (n; s) Davenport{Schinzel sequence, for positive integers n and s, is a sequence composed of n distinct symbols with the properties that no two adjacent elements are equal, and that it does not contain, as a (possibly non-contiguous) subsequence, any alternation a b a b of length s + 2 between two distinct symbols a and b. The close relationship between(More)
We propose a mathematical formulation for the notion of optimal projective cluster, starting from natural requirements on the density of points in subspaces. This allows us to develop a Monte Carlo algorithm for iteratively computing projective clusters. We prove that the computed clusters are good with high probability. We implemented a modified version of(More)
Motivated by the problem of labeling maps, we i n vestigate the problem of computing a large non-intersecting subset in a set of n rectangles in the plane. Our results are as follows. In On log n time, we can nd an Olog n-factor approximation of the maximum subset in a set of n arbitrary axis-parallel rectangles in the plane. If all rectangles have unit(More)
We present a general technique for approximating various descriptors of the extent of a set <i>P</i> of <i>n</i> points in R<sup><i>d</i></sup> when the dimension <i>d</i> is an arbitrary fixed constant. For a given extent measure &mu; and a parameter &epsiv; &gt; 0, it computes in time <i>O</i>(<i>n</i> + 1/&epsiv;<sup><i>O</i>(1)</sup>) a subset <i>Q</i>(More)
We propose the idea of simplification envelopes for generating a hierarchy of level-of-detail approximations for a given polygonal model. Our approach guarantees that all points of an approximation are within a user-specifiable distance from the original model and that all points of the original model are within a distance from the approximation.(More)
We propose three indexing schemes for storing a set S of N points in the plane, each moving along a linear trajectory, so that any query of the following form can be answered quickly: Given a rectangle R and a real value t; report all K points of S that lie inside R at time t: We first present an indexing structure that, for any given constant e > 0; uses(More)
We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, prune-and-search techniques for linear programming and related problems, and LP-type problems and their(More)
<italic>We present an algorithm to compute a Euclidean minimum spanning tree of a given set S of n points in</italic> @@@@<supscrpt><italic>d</italic></supscrpt> <italic>in time &Ogr;</italic>(<italic>&#932;<subscrpt>d</subscrpt></italic>(<italic>N, N</italic>) log<supscrpt><italic>d</supscrpt> N</italic>), <italic>where(More)