Real m-neighbor distance
Partha Pratim Das · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1993
The notion of m-Neighbor Distance dnm, 1 ≤ m ≤ n, m integer, in the n- D digital geometry has been extended under the name of real m-Neighbor Distance (delta) nm, in this paper, to n-D real space. Complete analyses of the hyperspheres H(m,n;r) of (delta) nm have been carried out to show that the maxima of the absolute and relative errors between this metric and the Euclidean norm En minimizes at certain extreme symmetric points on the hypersphere. The coherence between these results and those already available in the digital domain has been mentioned to project (delta) nm as a powerful tool in metric analyses in digital geometry. The paper also makes fundamental contributions in the study of non-Euclidean metric spaces, extending the L1 equals (delta) n1 and LINF equals (delta) nn norms in a natural yet non- Minkowski way. Finally it is shown that real m-neighbor distance has direct applications in scheduling problems.