Asymptotically tight bounds for (≤k)-sets are given, which are certain halfspace partitions of point sets, and a simple proof of Lee's bounds for high-order Voronoi diagrams is given.Expand

We design a new distribution over m × n matrices S so that, for any fixed n × d matrix A of rank r, with probability at least 9/10, ∥SAx∥2 = (1 ± ε)∥Ax∥2 simultaneously for all x ∈ Rd. Here, m is… Expand

Near-optimal space bounds are given in the streaming model for linear algebra problems that include estimation of matrix products, linear regression, low-rank approximation, and approximation of matrix rank; results for turnstile updates are proved.Expand

It is shown that any point-set has an ∊-core-set of size [2/∊], and a fast algorithm is given that finds this core-set and implies the existence of small core-sets for solving approximate approximate <i>k</i>-center clustering and related problems.Expand

This paper gives several new demonstrations of the usefulness of random sampling techniques in computational geometry. One new algorithm creates a search structure for arrangements of hyperplanes by… Expand

This paper gives approximation algorithms of solving the following motion planning problem: Given a set of polyhedral obstacles and points s and t, find a shortest path from s to t that avoids the… Expand

It is shown that polynomial-time approximation algorithms with provable performance exist, under a certain general condition: that for a random subset $R\subset S$ and nondecreasing function f(·), there is a decomposition of the complement ${Bbb U}\backslash\bigcup (R)$ into an expected at most f(|R|) regions, each region of a particular simple form.Expand

An algorithm for solving linear programming problems with n constraints and d variables and the number of bits required to specify the rational numbers defining an input constraint or the objective function vector is given.Expand