Instance-optimal geometric algorithms

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2009, Pages 129-138

  Afshani, Peyman ^a   Barbay, Jérémy ^b   Chan, Timothy M ^c  

^a AARHUS UNIVERSITY   (Denmark)

^b UNIVERSITY OF CHILE   (Chile)

^c UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Adaptive algorithms; Computational geometry; Convex hull; Decision trees; Entropy sensitive data structures; Instance optimality; Lower bounds; Maxima; Orthogonal segment intersection; Output sensitive algorithms; Point location

Indexed keywords

CONVEX HULL; LOWER BOUNDS; OPTIMALITY; ORTHOGONAL SEGMENT INTERSECTION; ORTHOGONAL SEGMENTS; OUTPUT-SENSITIVE ALGORITHM; POINT LOCATION; SENSITIVE DATAS;

COMPUTATION THEORY; COMPUTATIONAL GEOMETRY; DATA STRUCTURES; DECISION TREES; ENTROPY; FIBER OPTIC CHEMICAL SENSORS; OPTIMIZATION;

ADAPTIVE ALGORITHMS;

EID: 77952344373     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2009.34     Document Type: Conference Paper

References (40)

1. D. S. Andrews, J. Snoeyink, J. Boritz, T. Chan, G. Denham, J. Harrison, and C. Zhu, "Further comparisons of algorithms for geometric intersection problems," in Proc. 6th International Symposium on Spatial Data Handling, 1994, pp. 709-724.
2. S. Arya, T. Malamatos, and D. M. Mount, "A simple entropy-based algorithm for planar point location," ACM Transactions on Algorithms, vol. 3, no. 2, p. 17, 2007.
3. S. Arya, T. Malamatos, D. M. Mount, and K. C. Wong, "Optimal expected-case planar point location," SIAM Journal on Computing, vol. 37, no. 2, pp. 584-610, 2007.
4. I. Baran and E. D. Demaine, "Optimal adaptive algorithms for finding the nearest and farthest point on a parametric black-box curve," International Journal of Computational Geometry and Applications, vol. 15, no. 4, pp. 327-350, 2005.
5. I. Baran, E. D. Demaine, and D. A. Katz, "Optimally adaptive integration of univariate Lipschitz functions," Algorithmica, vol. 50, no. 2, pp. 255-278, 2008.
6. J. Barbay and E. Chen, "Adaptive planar convex hull algorithm for a set of convex hulls," in Proc. 20th Canadian Conference on Computational Geometry, 2008, pp. 47-50.
7. M. Ben-Or, "Lower bounds for algebraic computation trees," in Proc. 15th ACM Symposium on Theory of Computing, 1983, pp. 80-86.
8. J. L. Bentley, K. L. Clarkson, and D. B. Levine, "Fast linear expected-time algorithms for computing maxima and convex hulls," in Proc. 1st ACM-SIAM Symposium on Discrete Algorithms, 1990, pp. 179-187.
9. B. K. Bhattacharya and S. Sen, "On a simple, practical, optimal, output-sensitive randomized planar convex hull algorithm," Journal of Algorithms, vol. 25, no. 1, pp. 177-193, 1997.
10. J. Boyar and L. M. Favrholdt, "The relative worst order ratio for online algorithms," ACM Transactions on Algorithms, vol. 3, no. 2, p. 22, May 2007.
11. T. M. Chan, "Ω(n log n) lower bounds made easy," University of Waterloo, Note, in preparation.
12. -, "Optimal output-sensitive convex hull algorithms in two and three dimensions," Discrete and Computational Geometry, vol. 16, pp. 361-368, 1996.
13. -, "Output-sensitive results on convex hulls, extreme points, and related problems," Discrete and Computational Geometry, vol. 16, pp. 369-387, 1996.
14. -, "Comparison-based time-space lower bounds for selection," in Proc. 20th ACM-SIAM Symposium on Discrete Algorithms, 2009, pp. 140-149.
15. T. M. Chan, J. Snoeyink, and C.-K. Yap, "Primal dividing and dual pruning: Output-sensitive construction of four-dimensional polytopes and three-dimensional Voronoi diagrams," Discrete and Computational Geometry, vol. 18, pp. 433-454, 1997.
16. B. Chazelle and J. Matoušek, "Derandomizing an output-sensitive convex hull algorithm in three dimensions," Computational Geometry: Theory and Applications, vol. 5, pp. 27-32, 1995.
17. K. L. Clarkson, "More output-sensitive geometric algorithms," in Proc. 35th IEEE Symposium on Foundations of Computer Science, 1994, pp. 695-702.
18. K. L. Clarkson and P. W. Shor, "Applications of random sampling in computational geometry, II," Discrete and Computational Geometry, vol. 4, pp. 387-421, 1989.
19. S. Collette, V. Dujmović, J. Iacono, S. Langerman, and P. Morin, "Distribution-sensitive point location in convex subdivisions," in Proc. 19th ACM-SIAM Symposium on Discrete Algorithms, 2008, pp. 912-921, see also http://arxiv.org/abs/0901.1908.
20. P. Dagum, R. M. Karp, M. Luby, and S. M. Ross, "An optimal algorithm for Monte Carlo estimation," SIAM Journal on Computing, vol. 29, no. 5, pp. 1484-1496, 2000.
21. M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf, Computational Geometry: Algorithms and Applications. Springer-Verlag, 1997.
22. E. D. Demaine, D. Harmon, J. Iacono, D. Kane, and M. Pǎtraş cu, "The geometry of binary search trees," in Proc. 20th ACM-SIAM Symposium on Discrete Algorithms, 2009, pp. 496-505.
23. E. D. Demaine, A. López-Ortiz, and J. I. Munro, "Adaptive set intersections, unions, and differences," in Proc. 11th ACM-SIAM Symposium on Discrete Algorithms, 2000, pp. 743-752.
24. V. Dujmović, J. Howat, and P. Morin, "Biased range trees," in Proc. 20th ACM-SIAM Symposium on Discrete Algorithms, 2009, pp. 486-495.
25. H. Edelsbrunner, Algorithms in Combinatorial Geometry. Springer-Verlag, 1987.
26. 2 h) time algorithm for the three-dimensional convex hull problem," SIAM Journal on Computing, vol. 20, no. 2, pp. 259-269, 1990.
27. R. Fagin, A. Lotem, and M. Naor, "Optimal aggregation algorithms for middleware," Journal of Computer and System Sciences, vol. 66, no. 4, pp. 614-656, 2003.
28. J. Iacono, "Expected asymptotically optimal planar point location," Computational Geometry: Theory and Applications, vol. 29, pp. 19-22, 2004.
29. C. Kenyon, "Best-fit bin-packing with random order," in Proc. 7th ACM-SIAM Symposium on Discrete Algorithms, 1996, pp. 359-364.
30. D. G. Kirkpatrick and R. Seidel, "The ultimate planar convex hull algorithm?" SIAM Journal on Computing, vol. 15(1), pp. 287-299, 1986.
31. -, "Output-size sensitive algorithms for finding maximal vectors," in Proc. 1st ACM Symposium on Computational Geometry, 1985, pp. 89-96.
32. J. Matoušek, "Efficient partition trees," Discrete and Computational Geometry, vol. 8, no. 3, pp. 315-334, 1992.
33. S. Moran, M. Snir, and U. Manber, "Applications of Ramsey's theorem to decision tree complexity," Journal of the ACM, vol. 32, no. 4, pp. 938-949, 1985.
34. J. I. Munro and P. M. Spira, "Sorting and searching in multisets," SIAM Journal on Computing, vol. 5, no. 1, pp. 1-8, 1976.
35. F. P. Preparata and M. I. Shamos, Computational Geometry: An Introduction. Springer-Verlag, 1985.
36. S. Sen and N. Gupta, "Distribution-sensitive algorithms," Nordic Journal on Computing, vol. 6, pp. 194-211, 1999.
37. D. D. Sleator and R. E. Tarjan, "Self-adjusting binary search trees," Journal of the ACM, vol. 32, no. 3, pp. 652-686, 1985.
38. R. Wenger, "Randomized quickhull," Algorithmica, vol. 17, pp. 322-329, 1997.
39. A. C.-C. Yao, "A lower bound to finding convex hulls," Journal of the ACM, vol. 28, pp. 780-787, 1981.
40. -, "Lower bounds for algebraic computation trees with integer inputs," SIAM Journal on Computing, vol. 20, no. 4, pp. 655-668, 1991.