The number of congruent simplices in a point set

Discrete and Computational Geometry

Volumn 28, Issue 2, 2002, Pages 123-150

  Agarwal, Pankaj K ^a   Sharir, Micha ^b,c  

^a Duke University   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036025568     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-002-0727-x     Document Type: Article

References (27)

1. B. M. Ábrego, G. Elekes, and S. Fernándes-Merchant, Structural results for plane sets with many similar subsets, Combinatorica 21 (2001), to appear.
2. B. M Ábrego and S. Fernándes-Merchant, On the maximum number of equilateral triangles, I, Discrete Comput. Geom. 23 (2000), 129-135.
3. B. M. Ábrego and S. Fernándes-Merchant, On the maximum number of equilateral triangles, II, Discrete Comput. Geom., to appear.
4. P. K. Aganval, J. Matoušek, and O. Schwarzkopf, Computing many faces in arrangements of lines and segments, SIAM J. Comput. 27 (1998), 491-505.
5. T. Akutsu, H. Tamaki, and T. Tokuyama, Distribution of distances and triangles in a point set and algorithms for computing the largest common point set, Discrete Comput. Geom. 20 (1998), 307-331.
6. B. Aronov, V. Koltun, and M. Sharir, Incidences between points and circles in three and higher dimensions, manuscript, 2002.
7. B. Aronov, M. Pellegrini, and M. Sharir, On the zone of a surface in a hyperplane arrangement, Discrete Comput, Geom. 9 (1993), 177-186.
8. B. Aronov and M. Sharir, Cutting circles into pseudo-segments and improved bounds on incidences, Discrete Comput. Geom., in press.
9. L. Boxer, Point set pattern matching in 3-D, Pattern Recognition Lett. 17 (1996), 1293-1297.
10. P. Brass, Exact point pattern matching and the number of congruent triangles in a three-dimensional point set, Proc. European Sympos. Algorithms, Lecture Notes in Computer Science, vol. 1879, Springer-Verlag, Berlin, 2000, pp. 112-119.
11. P. Brass and C. Knauer, Testing the congruence of d-dimensional point sets, Proc. 16th Annu. ACM Sympos. Comput. Geom., 2000, pp. 310-314.
12. H. Brönnimann, B. Chazelle, and J. Matoušek, Product range spaces, sensitive sampling, and derandomization, SIAM J. Comput. 28 (1999), 1552-1575.
13. B. Chazelle, Cutting hyperplanes for divide-and-conquer, Discrete Comput. Geom. 9 (1993), 145-158.
14. B. Chazelle and J. Friedman, A deterministic view of random sampling and its use in geometry, Combinatorica 10 (1990), 229-249.
15. K. Clarkson, H. Edelsbrunner, L. Guibas, M. Sharir, and E. Welzl, Combinatorial complexity bounds for arrangements of curves and spheres, Discrete Comput. Geom. 5 (1990), 99-160.
16. H. Edelsbrunner. Algorithms in Combinatorial Geometry, Springer-Verlag, Heidelberg, 1987.
17. P. Erdos, On a set of distances of n points, Amer. Math. Monthly 53 (1946), 248-250.
18. P. Erdos, D. Hickerson, and J. Pach, A problem of Leo Moser about repeated distances on the sphere, Amer. Math. Monthly 96 (1989), 569-575.
19. P. Erdos and G. Purdy, Some extremal problems in geometry, III, Proc. 6th South-Eastern Conf. Combin. Graph Theory Comput., 1975, pp. 291-308.
20. P. Erdos and G. Purdy. Some extremal problems in geometry, IV, Proc. 7th South-Eastern Conf. Combin. Graph Theory Comput., 1976, pp. 307-322.
21. J. Matoušek, Range searching with efficient hierarchical cuttings, Discrete Comput. Geom. 10 (1993), 157-182.
22. G. L. Nemhauser and L. A. Wolsey, Integer and Commbinatorial Optimization, Wiley Interscience, New York, 1988.
23. J. Pach and P. K. Agarwal, Combinatorial Geometry, Wiley Interscience, New York, 1995.
24. P. J. de Rezende and D.-T. Lee, Point set pattern matching in d-dimensons, Algorithmica 13 (1995), 387-404.
25. M. Sharir and P. K. Agarwal, Davenport-Schinzel Sequences and Their Geometric Applications, Cambridge University Press, Cambridge, 1995.
26. J. Spencer, E. Szemerédi, and W. Trotter, Unit distances in the Euclidean plane, in: Graph Theory and Combinatorics (Proc. Cambridge Conf. on Combinatorics, B. Bollobas, ed.), Academic Press, New York, 1984, pp. 293-308.
27. L. A. Székely, Crossing numbers and hard Erdos problems in discrete geometry, Combin. Probab. Comput. 6 (1997), 353-358.