On the size of a random sphere of influence graph

Advances in Applied Probability

Volumn 31, Issue 3, 1999, Pages 596-609

  Chalker, T K ^a,e   Godbole, A P ^a,d   Hitczenko, P ^a,c   Radcliff, J ^a   Ruehr, O G ^b,c,d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Michigan Technological University   (United States)

^c NORTH CAROLINA STATE UNIVERSITY   (United States)

^d UNIVERSITY OF MICHIGAN   (United States)

^e MICHIGAN TECHNOLOGICAL UNIVERSITY   (United States)

Author keywords

Azuma Hoeffding inequality; Random graphs; Sphere of influence graphs

Indexed keywords

EID: 0033184512     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800009307     Document Type: Article

References (11)

1. AVIS, D. AND HORTON, J. (1985). Remarks on the sphere of influence graph. In Discrete Geometry and Convexity, ed. J. E. Goodman et al. New York Academy of Sciences, New York, pp. 323-327.
2. CHALKER, T. K. AND RADCLIFF, J. (1995). REU Project Report, Michigan Tech University.
3. DWYER, R. A. (1995). The expected size of the sphere-of-influence graph. Computational Geometry: Theory and Applications 5, 155-164.
4. FÜREDI, Z. AND LOEB, P. A. (1994). On the best constant for the Besicovitch covering theorem. Proc. Amer. Math. Soc. 121, 1063-1073.
5. GUIBAS, L., PACH, J. AND SHARIR, M. (1994). Sphere-of-influence graphs in higher dimensions. In Intuitive Geometry, Colloq. Math. Soc. János Bolyai 63, eds. K. Böröczky and G. Töth. János Bolyai Mathematical Society, Budapest, pp. 131-137.
6. HALL, P. (1988). Introduction to the Theory of Coverage Processes. Wiley, New York.
7. MICHAEL, T. S. AND QUINT, T. (1994). Sphere of influence graphs: a survey. Congressus Numerantium 105, 153-160.
8. n.pCombinatorial, 121-129.
9. STEELE, J. M. (1997). Probability TJieory and Combinatorial Optimization (NSF-CBMS Regional Research Conference Lecture Notes Series Vol. 69). Society for Industrial and Applied Mathematics, Philadelphia, PA.
10. TALAGRAND, M. (1995). Concentration of measure and isoperimetric inequalities in product spaces. Publications Malh.IHES 81, 73-205.
11. TOUSSAINT, G. T. (1980). Pattern recognition and geometric complexity. In Proceedings of the 5th International Conference on Pattern Recognition, pp. 1324-1347. IEEE Computer Society Press, Washington DC.