Geodesic
On a sphere of influence graph in a one-dimensional space
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 427-433.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: cluster, sphere of influence graph 
@article{DMGT_2005_25_3_a18,
     author = {Palka, Zbigniew and Sperling, Monika},
     title = {On a sphere of influence graph in a one-dimensional space},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {427--433},
     publisher = {mathdoc},
     volume = {25},
     number = {3},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a18/}
}
TY  - JOUR
AU  - Palka, Zbigniew
AU  - Sperling, Monika
TI  - On a sphere of influence graph in a one-dimensional space
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2005
SP  - 427
EP  - 433
VL  - 25
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a18/
LA  - en
ID  - DMGT_2005_25_3_a18
ER  - 
%0 Journal Article
%A Palka, Zbigniew
%A Sperling, Monika
%T On a sphere of influence graph in a one-dimensional space
%J Discussiones Mathematicae. Graph Theory
%D 2005
%P 427-433
%V 25
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a18/
%G en
%F DMGT_2005_25_3_a18
Palka, Zbigniew; Sperling, Monika. On a sphere of influence graph in a one-dimensional space. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 427-433. http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a18/

[1] P. Avis and J. Horton, Remarks on the sphere of influence graph, in: ed. J.E. Goodman, et al. Discrete Geometry and Convexity (New York Academy of Science, New York) 323-327.

[2] T. Chalker, A. Godbole, P. Hitczenko, J. Radcliff and O. Ruehr, On the size of a random sphere of influence graph, Adv. in Appl. Probab. 31 (1999) 596-609, doi: 10.1239/aap/1029955193.

[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.

[4] Z. Furedi, The expected size of a random sphere of influence graph, Intuitive Geometry, Bolyai Math. Soc. 6 (1995) 319-326.

[5] Z. Furedi and P.A. Loeb, On the best constant on the Besicovitch covering theorem, in: Proc. Coll. Math. Soc. J. Bolyai 63 (1994) 1063-1073.

[6] P. Hitczenko, S. Janson and J.E. Yukich, On the variance of the random sphere of influence graph, Random Struct. Alg. 14 (1999) 139-152, doi: 10.1002/(SICI)1098-2418(199903)14:2139::AID-RSA2>3.0.CO;2-E

[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.

[8] T.S. Michael and T. Quint, Sphere of influence graphs: a survey, Congr. Numer. 105 (1994) 153-160.

[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.

[10] Toussaint, Pattern recognition of geometric complexity, in: Proceedings of the 5th Int. Conference on Pattern Recognition, (1980) 1324-1347.

[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.