Sigma-local graphs

Journal of Discrete Algorithms

Volumn 8, Issue 1, 2010, Pages 15-23

  Bose, Prosenjit ^a   Collette, Sébastien ^b   Langerman, Stefan ^b   Maheshwari, Anil ^a   Morin, Pat ^a   Smid, Michiel ^a  

^a CARLETON UNIVERSITY   (Canada)

^b UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Geometric graphs; Proximity graphs

Indexed keywords

GEOMETRIC GRAPHS; ISOLATED VERTICES; PLANARITY; PROXIMITY GRAPHS; REAL NUMBER;

ALGORITHMS; COMPUTATION THEORY; COMPUTATIONAL EFFICIENCY; COMPUTATIONAL GEOMETRY; NUMBER THEORY;

SET THEORY;

EID: 70350585213     PISSN: 15708667     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jda.2008.10.002     Document Type: Article

References (24)

1. Agarwal P. Range searching. In: Goodman J.E., and O'Rourke J. (Eds). Handbook of Discrete and Computational Geometry (2004), CRC Press LLC, Boca Raton, FL 809-837 (Chapter 36)
2. Agarwal P., and Matoušek J. Relative neighborhood graphs in three dimensions. Computational Geometry: Theory and Applications 2 (1992) 1-14
3. Aggarwal A., Hansen M., and Leighton T. Solving query-retrieval problems by compacting Voronoi diagrams. STOC '90: Proceedings of the Twenty-Second Annual ACM Symposium on Theory of Computing (1990), ACM Press, New York 331-340
4. Amato N.M., and Preparata F.P. A time-optimal parallel algorithm for three-dimensional convex hulls. Algorithmica 14 2 (1995) 169-182
5. Bentley J.L., and Ottmann T.A. Algorithms for reporting and counting geometric intersections. IEEE Transactions on Computers C-28 9 (1979) 643-647
6. Boruvka O. O jistem problemu minimalnim. Prace Moravske Prirodovedecke Spolecnosti 3 (1926) 37-58
7. Bose P., Devroye L., Evans W., and Kirkpatrick D. On the spanning ratio of Gabriel graphs and β-skeleton. SIAM Journal on Discrete Mathematics 20 2 (2006) 412-427
8. Callahan P.B., and Kosaraju S.R. A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields. Journal of the ACM 42 1 (1995) 67-90
9. J. Cardinal, S. Collette, S. Langerman, Region counting graphs, in: Proceedings of the European Workshop on Computational Geometry (EWCG05), 2005
10. Dobkin D., and Kirkpatrick D. Fast detection of poyhedral intersection. Theoretical Computer Science 27 (1983) 241-253
11. Eppstein D., Paterson M., and Yao F. On nearest-neighbor graphs. Discrete and Computational Geometry 17 (1997) 263-282
12. Erickson J. Local polyhedra and geometric graphs. Computational Geometry: Theory and Applications 31 1-2 (2005) 101-125
13. Gabriel K., and Sokal R. A new statistical approach to geographic variation analysis. Systematic Zoology 18 (1969) 259-278
14. Ichino M., and Sklansky J. The relative neighborhood graph for mixed feature variables. Pattern Recognition 18 (1985) 161-167
15. Jaromczyk J., and Toussaint G. Relative neighborhood graphs and their relatives. Proceedings of the IEEE 80 9 (1992) 1502-1571
16. Keil J., and Gutwin C. Classes of graphs which approximate the complete Euclidean graph. Discrete and Computational Geometry 7 1 (1992) 13-28
17. Kirkpatrick D., and Radke J. A framework for computational morphology. Computational Geometry (1985) 217-248
18. Matula D., and Sokal R. Properties of Gabriel graphs relevant to geographic variation research and the clustering of points in the plane. Geographical Analysis 12 (1980) 205-222
19. Megiddo N. Applying parallel computation algorithms in the design of serial algorithms. Journal of the ACM 30 4 (1983) 852-865
20. Motwani R., and Raghavan P. Randomized Algorithms (1995), Cambridge University Press
21. Reif J.H., and Sen S. Optimal parallel randomized algorithms for three-dimensional convex hulls and related problems. SIAM Journal on Computing 21 3 (1992) 466-485
22. Vaidya P.M. An O (n log n) algorithm for the all-nearest neighbors problem. Discrete & Computational Geometry 4 (1989) 101-115
23. Veltkamp R. The γ-neighbourhood graph. Computational Geometry: Theory and Applications 1 (1992) 227-246
24. Yao A. On constructing minimum spanning trees in k-dimensional spaces and related problems. SIAM Journal on Computing 11 4 (1982) 721-736