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...

Full description

Saved in:
Bibliographic Details
Published in:Moscow University computational mathematics and cybernetics Vol. 34; no. 4; pp. 164 - 171
Main Author: Karpovich, P. A.
Format: Journal Article
Language:English
Published: Heidelberg Allerton Press, Inc 01.12.2010
Subjects:
Mathematics
Mathematics and Statistics
combinatorial optimization
estimate calculation algorithms
ISSN:0278-6419, 1934-8428
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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