A linear time deterministic algorithm to find a small subset that approximates the centroid

Given a set of points S in any dimension, we describe a deterministic algorithm for finding a T ⊂ S , | T | = O ( 1 / ε ) such that the centroid of T approximates the centroid of S within a factor 1 + ε for any fixed ε > 0 . We achieve this in linear time by an efficient derandomization of the al...

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Veröffentlicht in:Information processing letters Jg. 105; H. 1; S. 17 - 19
Hauptverfasser: Worah, Pratik, Sen, Sandeep
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 31.12.2007
Elsevier Science
Elsevier Sequoia S.A
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Artificial intelligence
Clustering
Computational geometry
Computer science; control theory; systems
Derandomization
Exact sciences and technology
Geometry
Mathematics
Miscellaneous
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Pattern recognition. Digital image processing. Computational geometry
Random variables
Sciences and techniques of general use
Studies
Theoretical computing
Clustering
Computational geometry
Derandomization
Voronoï diagram
Randomization
Computer theory
Information processing
Linear time
Application
Algorithm analysis
Variance
Deterministic algorithms
ISSN:0020-0190, 1872-6119
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:Given a set of points S in any dimension, we describe a deterministic algorithm for finding a T ⊂ S , | T | = O ( 1 / ε ) such that the centroid of T approximates the centroid of S within a factor 1 + ε for any fixed ε > 0 . We achieve this in linear time by an efficient derandomization of the algorithm in [M. Inaba, N. Katoh, H. Imai, Applications of weighted Voronoi diagrams and randomization to variance-based k-clustering (extended abstract), in: Proceedings of the Tenth Annual Symposium on Computational Geometry, 1994, pp. 332–339].
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2007.07.008