On a sphere of influence graph in a one-dimensional space

Zbigniew Palka; Monika Sperling

Discussiones Mathematicae Graph Theory (2005)

  • Volume: 25, Issue: 3, page 427-433
  • ISSN: 2083-5892

Abstract

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A sphere of influence graph generated by a finite population of generated points on the real line by a Poisson process is considered. We determine the expected number and variance of societies formed by population of n points in a one-dimensional space.

How to cite

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Zbigniew Palka, and Monika Sperling. "On a sphere of influence graph in a one-dimensional space." Discussiones Mathematicae Graph Theory 25.3 (2005): 427-433. <http://eudml.org/doc/270198>.

@article{ZbigniewPalka2005,
abstract = {A sphere of influence graph generated by a finite population of generated points on the real line by a Poisson process is considered. We determine the expected number and variance of societies formed by population of n points in a one-dimensional space.},
author = {Zbigniew Palka, Monika Sperling},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {cluster; sphere of influence graph},
language = {eng},
number = {3},
pages = {427-433},
title = {On a sphere of influence graph in a one-dimensional space},
url = {http://eudml.org/doc/270198},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Zbigniew Palka
AU - Monika Sperling
TI - On a sphere of influence graph in a one-dimensional space
JO - Discussiones Mathematicae Graph Theory
PY - 2005
VL - 25
IS - 3
SP - 427
EP - 433
AB - A sphere of influence graph generated by a finite population of generated points on the real line by a Poisson process is considered. We determine the expected number and variance of societies formed by population of n points in a one-dimensional space.
LA - eng
KW - cluster; sphere of influence graph
UR - http://eudml.org/doc/270198
ER -

References

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  3. [3] E.G. Enns, P.F. Ehlers and T. Misi, A cluster problem as defined by nearest neighbours, The Canadian Journal of Statistics 27 (1999) 843-851, doi: 10.2307/3316135. Zbl0949.60030
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  7. [7] L. Guibas, J. Pach and M. Sharir, Sphere of influence graphs in higher dimensions, in: Proc. Coll. Math. Soc. J. Bolyai 63 (1994) 131-137. Zbl0821.52003
  8. [8] T.S. Michael and T. Quint, Sphere of influence graphs: a survey, Congr. Numer. 105 (1994) 153-160. Zbl0835.05078
  9. [9] T.S. Michael and T. Quint, Sphere of influence graphs and the L_∞-metric, Discrete Appl. Math. 127 (2003) 447-460, doi: 10.1016/S0166-218X(02)00246-9. Zbl1018.05094
  10. [10] Toussaint, Pattern recognition of geometric complexity, in: Proceedings of the 5th Int. Conference on Pattern Recognition, (1980) 1324-1347. 
  11. [11] D. Warren and E. Seneta, Peaks and eulerian numbers in a random sequence, J. Appl. Prob. 33 (1996) 101-114, doi: 10.2307/3215267. Zbl0845.60035

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