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

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1. [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. Zbl0573.52013
2. [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. Zbl0944.60019
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
4. [4] Z. Furedi, The expected size of a random sphere of influence graph, Intuitive Geometry, Bolyai Math. Soc. 6 (1995) 319-326. Zbl0881.05113
5. [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. Zbl0802.28002
6. [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 Zbl0922.60025
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