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» K -Trivial Closed Sets and Continuous Functions
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JSYML
2000
76views more  JSYML 2000»
13 years 4 months ago
Located Sets and Reverse Mathematics
Let X be a compact metric space. A closed set K X is located if the distance function d(x, K) exists as a continuous realvalued function on X; weakly located if the predicate d(x,...
Mariagnese Giusto, Stephen G. Simpson
JUCS
2008
140views more  JUCS 2008»
13 years 4 months ago
The Computable Multi-Functions on Multi-represented Sets are Closed under Programming
: In the representation approach to computable analysis (TTE) [Grz55, i00], abstract data like rational numbers, real numbers, compact sets or continuous real functions are represe...
Klaus Weihrauch
RC
2006
69views more  RC 2006»
13 years 4 months ago
The Set of Hausdorff Continuous Functions - The Largest Linear Space of Interval Functions
Hausdorff continuous (H-continuous) functions are special interval-valued functions which are commonly used in practice, e.g. histograms are such functions. However, in order to av...
Roumen Anguelov, Svetoslav Markov, Blagovest Sendo...
FOCS
2010
IEEE
13 years 2 months ago
Stability Yields a PTAS for k-Median and k-Means Clustering
We consider k-median clustering in finite metric spaces and k-means clustering in Euclidean spaces, in the setting where k is part of the input (not a constant). For the k-means pr...
Pranjal Awasthi, Avrim Blum, Or Sheffet
JAT
2011
93views more  JAT 2011»
12 years 11 months ago
Approximation theorems for group valued functions
Stone-Weierstrass-type theorems for groups of group-valued functions with discrete range or discrete domain are obtained. We study criteria for a subgroup of the group of continuou...
Jorge Galindo, Manuel Sanchis