On the variance of the random sphere of influence graph

Random Structures and Algorithms

Volumn 14, Issue 2, 1999, Pages 139-152

  Hitczenko, P ^a   Janson, S ^b   Yukich, J E ^c  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b UPPSALA UNIVERSITY   (Sweden)

^c LEHIGH UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033477037     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2418(199903)14:2<139::AID-RSA2>3.0.CO;2-E     Document Type: Article

References (16)

1. F. Avram and D. Bertsimas, On central limit theorems in geometric probability, Ann Appl Probab 3 (1993), 1033-1046.
2. P. Baldi and Y. Rinott, On normal approximations of distributions in terms of dependency graphs, Ann Probab 17 (1989), 1646-1650.
3. T.K. Chalker, A.P. Godbole, P. Hitczenko, J. Radcliff, and O.G. Ruehr, On the size of a random sphere of influence graph, preprint, 1997.
4. L. Devroye, The expected size of some graphs in computational geometry, Comput Math Appl 15 (1988), 53-64.
5. R.A. Dwyer, The expected size of the sphere of influence graph, Comp Geometry 5 (1995), 155-164.
6. B. Efron and C. Stein, The jackknife estimate of variance, Ann Statist 9 (1981), 586-596.
7. Z. Füredi, The expected size of a random sphere of influence graph, Intuitive Geometry, Bolyai Mathematical Society, 6 (1995), 319-326.
8. P. Groeneboom, Limit theorems for convex hulls, Probab Theory Related Fields 79 (1988), 327-368.
9. S. Janson, Normal convergence by higher semiinvariants with applications to sums of dependent random variables and random graphs, Ann Probab 16 (1988), 305-312.
10. T.S. Michael and T. Quint, Sphere of influence graphs: a survey, Congress Number 105 (1994), 153-160.
11. M. Petrovskaya and A. Leontovitch, The central limit theorem for a sequence of random variables with a slowly growing number of dependencies, Theory Probab Appl 27 (1982), 815-825.
12. F.P. Preparata and M.I. Shamos, Computational geometry. An introduction, Springer-Verlag, Berlin/New York, 1985.
13. J.M. Steele, Probability theory and combinatorial optimization, NSF-CBMS Regional Research Conference Lecture Notes Series, Vol. 69, Society for Industrial and Applied Mathematics, SIAM, Philadelphia, PA, 1997.
14. J.M. Steele, "Variations on the monotone subsequence theme of Erdös and Szekeres," Discrete probability and algorithms, The IMA Volumes in Mathematics and Its Applications, Vol. 72, D. Aldous, P. Diaconis, J. Spencer, and J.M. Steele (Editors), Springer-Verlag, Berlin/New York, 1995.
15. G.T. Toussaint, Pattern recognition and geometric complexity, Proc 5th Int Conf Pattern Recognition, Miami Beach, FL, 1980, pp. 1324-1347.
16. J.E. Yukich, Probability theory of classical Euclidean optimization problems, Lecture Notes Math, Vol. 1675, Springer-Verlag, Berlin/New York, 1998.