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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)

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 μ and a parameter ϵ > 0, it computes in time <i>O</i>(<i>n</i> + 1/ϵ<sup><i>O</i>(1)</sup>) a subset <i>Q</i>… (More)

- Pankaj K. Agarwal, Je Erickson
- 1997

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 propose three indexing schemes for storing a set <italic>S</italic> of <italic>N</italic> points in the plane, each moving along a linear trajectory, so that a query of the following form can be answered quickly: Given a rectangle <italic>R</italic> and a real value <italic>t<subscrpt>q</subscrpt></italic>, report all <italic>K</italic> points of… (More)

- Jonathan D. Cohen, Amitabh Varshney, Dinesh Manocha, Greg Turk, Hans Weber, Pankaj K. Agarwal +2 others
- SIGGRAPH
- 1996

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)

<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>Τ<subscrpt>d</subscrpt></italic>(<italic>N, N</italic>) log<supscrpt><italic>d</supscrpt> N</italic>), <italic>where… (More)

Motivated by applications in computer graphics, visualization, and scientiic computation , we study the computational complexity of the following problem: Given a set S of n points sampled from a bivariate function f(x; y) and an input parameter " > 0, compute a piecewise-linear function (x; y) of minimum complexity (that is, a xy-monotone polyhedral… (More)