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2005 | 25 | 3 | 427-433
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Wydawca
Rocznik
Tom
25
Numer
3
Strony
427-433
Opis fizyczny
Daty
wydano
2005
otrzymano
2004-09-09
poprawiono
2005-05-04
Twórcy
  • Department of Algorithmics and Programming, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
  • Department of Algorithmics and Programming, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
Bibliografia
  • [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)14:2<139::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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1294
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