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FOCS
2003
IEEE
14 years 20 days ago
Bounded Geometries, Fractals, and Low-Distortion Embeddings
The doubling constant of a metric space (X, d) is the smallest value λ such that every ball in X can be covered by λ balls of half the radius. The doubling dimension of X is the...
Anupam Gupta, Robert Krauthgamer, James R. Lee
COMGEO
2008
ACM
13 years 7 months ago
Optimal core-sets for balls
Given a set of points P Rd and value > 0, an -core-set S P has the property that the smallest ball containing S is within of the smallest ball containing P. This paper shows ...
Mihai Badoiu, Kenneth L. Clarkson
ISAAC
1998
Springer
90views Algorithms» more  ISAAC 1998»
13 years 11 months ago
Generalized Self-Approaching Curves
Abstract. We consider all planar oriented curves that have the following property depending on a fixed angle . For each point B on the curve, the rest of the curve lies inside a we...
Oswin Aichholzer, Franz Aurenhammer, Christian Ick...
STOC
1993
ACM
76views Algorithms» more  STOC 1993»
13 years 11 months ago
Piecewise linear paths among convex obstacles
Let B be a set of n arbitrary possibly intersecting convex obstacles in Rd. It is shown that any two points which can be connected by a path avoiding the obstacles can also be c...
Mark de Berg, Jirí Matousek, Otfried Schwar...
STOC
2003
ACM
102views Algorithms» more  STOC 2003»
14 years 7 months ago
On metric ramsey-type phenomena
The main question studied in this article may be viewed as a nonlinear analogue of Dvoretzky's theorem in Banach space theory or as part of Ramsey theory in combinatorics. Gi...
Yair Bartal, Nathan Linial, Manor Mendel, Assaf Na...