• Publications
  • Influence
Optimal output-sensitive convex hull algorithms in two and three dimensions
  • Timothy M. Chan
  • Mathematics, Computer Science
  • Discret. Comput. Geom.
  • 1 April 1996
TLDR
We present simple output-sensitive algorithms that construct the convex hull of a set ofn points in two or three dimensions in worst-case optimal O (n logh) time andO (n) space, whereh denotes the number of vertices. Expand
  • 322
  • 20
  • PDF
Approximation algorithms for maximum independent set of pseudo-disks
TLDR
We present approximation algorithms for maximum independent set of pseudo-disks in the plane, both in the weighted and unweighted cases. Expand
  • 150
  • 19
  • PDF
Polynomial-time approximation schemes for packing and piercing fat objects
TLDR
We consider two problems: given a collection of n fat objects in a fixed dimension, (1) (packing) find the maximum subcollection of pairwise disjoint objects, and (2) (piercing)find the minimum point set that intersects every object. Expand
  • 173
  • 18
More Algorithms for All-Pairs Shortest Paths in Weighted Graphs
TLDR
In the first part of the paper, we reexamine the all-pairs shortest path (APSP) problem and present a new algorithm with running time $O(n^3log^3\log n/\log^2n)$, which improves all known algorithms for general real-weighted dense graphs. Expand
  • 96
  • 18
Optimal halfspace range reporting in three dimensions
TLDR
We give the first optimal solution to a standard problem in computational geometry: three-dimensional halfspace range reporting. Expand
  • 81
  • 16
An optimal randomized algorithm for maximum Tukey depth
TLDR
We present the first optimal algorithm to compute the maximumTukey depth (also known as <i>location or halfspace depth</i>) for a non-degenerate point set in the plane. Expand
  • 132
  • 15
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More planar two-center algorithms
TLDR
This paper describes further refinements of Sharir and Eppstein’s deterministic and randomized algorithms for the planar Euclidean two-center problem. Expand
  • 101
  • 14
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Faster core-set constructions and data-stream algorithms in fixed dimensions
TLDR
We speed up previous (1 + e)-factor approximation algorithms for a number of geometric optimization problems in fixed dimensions by improving the dependence of the "constants" in terms of e. Expand
  • 87
  • 14
  • PDF
Geometric applications of a randomized optimization technique
TLDR
We propose a simple, general, randomized technique to reduce certain geo- metric optimization problems to their corresponding decision problems. Expand
  • 80
  • 13
  • PDF
Low-Dimensional Linear Programming with Violations
TLDR
We present a simple algorithm in two dimensions that runs in O((n+k2)log n) expected time; this is faster than earlier algorithms by Everett, Robert, and van Kreveld (1993) and Matousek. Expand
  • 81
  • 11
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