The problem of maximizing a concave function <i>f</i>(<i>x</i>) in a simplex <S</i> can be solved approximately by a simple greedy algorithm, and several coreset bounds are generalized or strengthened.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

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 can be computed in O(nnz(A)) time, where nnz(A) is the number of nonzero entries of A.Expand

We design a new distribution over poly(r ε<sup>-1</sup>) x n matrices S so that for any fixed n x d matrix A of rank r, with probability at least 9/10, SAx<sub>2</sub> = (1 pm ε)Ax simultaneously for all x ∈ R.<sup>d</sup>.Expand

We give near-optimal space bounds in the streaming model for linear algebra problems that include estimation of matrix products, linear regression, low-rank approximation, and approximation of matrix rank.Expand

This paper gives approximation algorithms of solving the following motion planning problem: Given a set of polyhedral obstacles and points <italic>t</italic>, find a shortest path that avoids the obstacles.Expand