We describe dynamic data structures for half-space range reporting and for maintaining the minima of a decomposable function. Using these data structures, we obtain efficient dyna...
For a set S of points in Rd, an s-spanner is a graph on S such that any pair of points is connected via some path in the spanner whose total length is at most s times the Euclidea...
Let F be a collection of n d-variate, possibly partially defined, functions, all algebraic of some constant maximum degree. We present a randomized algorithm that computes the vert...
In this paper we give approximation algorithms for several proximity problems in high dimensional spaces. In particular, we give the rst Las Vegas data structure for (1 + )-neares...
We present a fully dynamic randomized data structure that can answer queries about the convex hull of a set of n points in three dimensions, where insertions take O(log3 n) expect...