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Optimal core-sets for balls
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 theExpand
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Approximate clustering via core-sets
TLDR
In this paper, we show that for several clustering problems one can extract a small set of points, so that using those core-sets enable us to perform approximate clustering efficiently. Expand
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Smaller core-sets for balls
TLDR
We show that any point-set has an ∊-core-set of size [2/∊]. Expand
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Approximation algorithms for low-distortion embeddings into low-dimensional spaces
TLDR
We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the two-dimensional plane. Expand
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A unified access bound on comparison-based dynamic dictionaries
TLDR
We present a dynamic comparison-based search structure that supports insertions, deletions, and searches within the unified bound. Expand
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Low-distortion embeddings of general metrics into the line
TLDR
A low-distortion embedding between two metric spaces is a mapping which preserves the distances between each pair of points, up to a small factor called distortion. Expand
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Facility Location in Sublinear Time
TLDR
We present a randomized constant factor approximation algorithm for the problem of computing the optimal cost of the metric Minimum Facility Location problem, in the case of uniform costs and uniform demands, in which every point can open a facility. Expand
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Approximation algorithms for embedding general metrics into trees
TLDR
We consider the problem of embedding general metrics into trees. Expand
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Low-Dimensional Embedding with Extra Information
TLDR
A frequently arising problem in computational geometry is when a physical structure, such as an ad-hoc wireless sensor network or a protein backbone, can measure local information about its geometry (e.g., distances, angles, and/or orientations), and the goal is to reconstruct the global geometry from this partial information. Expand
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Low-dimensional embedding with extra information
TLDR
A frequently arising problem in computational geometry is when a physical structure, such as an ad-hoc wireless sensor network or a protein backbone, can measure local information about its geometry, and the goal is to reconstruct the global geometry from this partial information. Expand
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