Criteria of the k-singularity and division of 1-singular systems

The concept of the k -singularity of systems of points in ℝ m space with l 1 metrics is studied. A system of q points is k -singular if and only if the dimensionality of the linear space of polynomials with powers no higher than the k of the columns of the matrix of pair-wise distances (element-wise...

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Veröffentlicht in:Moscow University computational mathematics and cybernetics Jg. 34; H. 4; S. 164 - 171
1. Verfasser: Karpovich, P. A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Heidelberg Allerton Press, Inc 01.12.2010
Schlagworte:
Mathematics
Mathematics and Statistics
combinatorial optimization
estimate calculation algorithms
ISSN:0278-6419, 1934-8428
Online-Zugang:Volltext
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Zusammenfassung:The concept of the k -singularity of systems of points in ℝ m space with l 1 metrics is studied. A system of q points is k -singular if and only if the dimensionality of the linear space of polynomials with powers no higher than the k of the columns of the matrix of pair-wise distances (element-wise multiplication) is strictly less than q . An algebraic criterion of k -singularity is obtained. The problem of dividing a system of points into subsystems that are not 1-singular is considered. An estimate of the minimum number of such subsystems is obtained.
ISSN:0278-6419
1934-8428
DOI:10.3103/S0278641910040035