Asymptotically tight bounds for a combinatorial quantity of interest in discrete and computational geometry, related to halfspace partitions of point sets, are 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

Given a set of points [email protected]?R^d and value @e>0, an @[email protected]?P has the property that the smallest ball containing S has radius within [email protected] of the radius of the… 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

The fastest known algorithms for overconstrained least-squares regression, low-rank approximation, approximating all leverage scores, and l<sub>p</sub>-regression are obtained.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

Upper and lower bounds for extremal problems defined for arrangements of lines, circles, spheres, and alike are presented and it is proved that the maximum number of edges boundingm cells in an arrangement ofn lines is Θ(m2/3n 2/3 +n), and that it isO(m3/2β(m) forn unit-circles.Expand