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FOCS
1992
IEEE
13 years 9 months ago
Dynamic Half-Space Reporting, Geometric Optimization, and Minimum Spanning Trees
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...
Pankaj K. Agarwal, David Eppstein, Jirí Mat...
COMPGEOM
2004
ACM
13 years 10 months ago
Deformable spanners and applications
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...
Jie Gao, Leonidas J. Guibas, An Nguyen
COMPGEOM
1994
ACM
13 years 9 months ago
Computing Envelopes in Four Dimensions with Applications
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...
Pankaj K. Agarwal, Boris Aronov, Micha Sharir
SODA
2000
ACM
127views Algorithms» more  SODA 2000»
13 years 6 months ago
Dimensionality reduction techniques for proximity problems
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...
Piotr Indyk
JACM
2010
135views more  JACM 2010»
13 years 3 months ago
A dynamic data structure for 3-D convex hulls and 2-D nearest neighbor queries
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...
Timothy M. Chan