Pankaj K. Agarwal

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About ten years ago, the eld of range searching, especially simplex range searching, was wide open. At that time, neither e cient algorithms nor nontrivial lower bounds were known for most range-searching problems. A series of papers by Haussler and Welzl [161], Clarkson [88, 89], and Clarkson and Shor [92] not only marked the beginning of a new chapter in(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 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)
Let P be a set of n points in ~d (where d is a small fixed positive integer), and let F be a collection of subsets of ~d, each of which is defined by a constant number of bounded degree polynomial inequalities. We consider the following F-range searching problem: Given P, build a data structure for efficient answering of queries of the form, "Given a 7 ~ F,(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)
In this paper we present an n^ O(k 1-1/d ) -time algorithm for solving the k -center problem in \reals d , under L ∈ fty - and L 2 -metrics. The algorithm extends to other metrics, and to the discrete k -center problem. We also describe a simple (1+ɛ) -approximation algorithm for the k -center problem, with running time O(nlog  k) + (k/ɛ)^ O(k 1-1/d ) .(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)