Almost-Delaunay Simplices: Nearest Neighbor Relations for Imprecise Points

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 15, Issue , 2004, Pages 403-412

  Bandyopadhyay, Deepak ^a   Snoeyink, Jack ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DELAUNAY SIMPLICES; IMPRECISE POINTS; NEAREST NEIGHBOR RELATIONS;

ALGORITHMS; CRYSTALLOGRAPHY; MATHEMATICAL TRANSFORMATIONS; NUCLEAR MAGNETIC RESONANCE; PERTURBATION TECHNIQUES; PROBLEM SOLVING; STRUCTURE (COMPOSITION); THEOREM PROVING;

PROTEINS;

EID: 1842435230     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (48)

1. Brookhaven protein data bank, http://www.rcsb.org.
2. M. Abellanas, F. Hurtado, and P. A. Ramos. Structural tolerance and Delaunay triangulation. Information Processing Letters, 71(5-6):221-227, 1999.
3. P. K. Agarwal, B. Aronov, S. Har-Peled, and M. Sharir. Approximation and exact algorithms for minimum-width annuli and shells. In Proc. 15th Annu. ACM Sympos. Comput. Geom., pages 380-389, 1999.
4. B. Angelov, J. Sadoc, R. Jullien, A. Soyer, J. Mornon, and J. Chomilier. Nonatomic solvent-driven Voronoi tessellation of proteins: an open tool to analyze protein folds. Proteins, 49(4):446-456, 2002.
5. F. Aurenhammer. Voronoi diagrams: A survey of a fundamental geometric data structure. ACM Comput. Surv., 23(3):345-405, 1991.
6. D. Bakowies and W. F. van Gunsteren. Water in protein cavities: A procedure to identify internal water and exchange pathways and application to fatty acid-binding protein. Proteins, 47(4): 534-545, 2002.
7. D. Bandyopadhyay, A. Tropsha, and J. Snoeyink. Almost-delaunay tetrahedra for analyzing protein structure, 2003. submitted. http://www.cs.unc.edu/~debug/ papers/AlmDel.
8. C. B. Barber, D. P. Dobkin, and H. Huhdanpaa. The Quick-hull algorithm for convex hulls. ACM Trans. Math. Softw., 22(4):469-483, 1996.
9. J.-D. Boissonnat and M. Yvinec. Algorithmic Geometry. Cambridge University Press, UK, 1998.
10. K. Q. Brown. Geometric transforms for fast geometric algorithms. PhD thesis, Carnegie-Mellon University, Pittsburgh, Penn., 1980.
11. C. W. Carter, B. C. LeFebvre, S. Cammer, A. Tropsha, and M. H. Edgell. Four-body potentials reveal protein-specific correlations to stability changes caused by hydrophobic core mutations. Journal of Molecular Biology, 311(4):625-638, 2001.
12. B. Chazelle and H. Edelsbrunner. An improved algorithm for constructing kth-order Voronoi diagrams. IEEE Trans. Comput., C-36:1349-1354, 1987.
13. M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational Geometry: Algorithms and Applications. Springer-Verlag, Berlin, Germany, 2nd edition, 2000.
14. B. Delaunay. Sur la sphère vide. A la memoire de Georges Voronoi. Izv.Akad. Nauk SSSR, Otdelenie Matematicheskih i Estestvennyh Nauk, 7:793-800, 1934.
15. C. A. Duncan, M. T. Goodrich, and E. A. Ramos. Efficient approximation and optimization algorithms for computational metrology. In Proc. 8th ACM-SIAM Sympos. Discrete Algorithms, pages 121-130, 1997.
16. R. A. Dwyer. Higher-dimensional voronoi diagrams in linear expected time. Discrete Comput. Geom., 6(4):343-367, 1991.
17. R. A. Dwyer. The expected number of k-faces of a voronoi diagram. Computers Math Applications, 26(5):13-19, 1993.
18. H. Ebara, N. Fukuyama, H. Nakano, and Y. Nakanishi. Roundness algorithms using the Voronoi diagrams. In Canadian Conference on Computational Geometry, page 41, 1989.
19. H. Edelsbrunner and E. P. Mücke. Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Trans. Graph., 9(1):66-104, 1990.
20. J. Garcia-Lopez, P. Ramos, and J. Snoeyink. Fitting a set of points by a circle. Discrete and Computational Geometry, 20:389-402, 1998.
21. J. Gudmundsson, M. Hammar, and M. J. van Kreveld. Higher order Delaunay triangulations. Comput. Geom.: Theory and Appl., 23(1):85-98, 2002.
22. L. J. Guibas, D. Salesin, and J. Stolfi. Epsilon geometry: building robust algorithms from imprecise computations. In Proc. 5th ACM Symp. Comp. Geom., pages 208-217, 1989.
23. B. Krishnamoorthy and A. Tropsha. Development of a four-body statistical pseudo-potential to discriminate native from non-native protein conformations. Bioinformatics, 19(12), 2003.
24. A. R. Leach. Molecular Modelling: Principles and Applications, second edition. Pearson Education EMA, UK, 2001.
25. A. M. Lesk. Introduction to Protein Architecture - The Structural Biology of Proteins. Oxford University Press, UK, 2000.
26. J. Liang and K. A. Dill. Are proteins well-packed? Biophys J., 81(2):751-766, 2001.
27. J. Liang, H. Edelsbrunner, P. Fu, P. Sudhakar, and S. Subramaniam. Analytical shape computing of macromolecules II: identification and computation of inaccessible cavities inside proteins. Proteins, 33:18-29, 1998.
28. J. Liang, H. Edelsbrunner, and C. Woodward. Anatomy of protein pockets and cavities: Measurement of binding site geometry and implications for ligand design. Protein Science, 7:1884-1897, 1998.
29. Y. C. Liao, D. J. Lee, and B.-H. Chen. Description of multi-particle systems using Voronoi polyhedra. Powder Technology, 119(2-3):81-88, 2001.
30. B. McConkey, V. Sobolev, and M. Edelman. Quantification of protein surfaces, volumes and atom-atom contacts using a constrained Voronoi procedure. Bioinformatics, 18(10): 1365-1373, 2002.
31. K. Mehlhorn, T. C. Shermer, and C.-K. Yap. A complete roundness classification procedure, in Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 129-138, 1997.
32. S. Miyazawa and R. L. Jernigan. Residue-residue potentials with a favorable contact pair term and an unfavorable high packing density term, for simulation and threading. Journal of Molecular Biology, 256:623-644, 1996.
33. P. J. Munson and R. K. Singh. Statistical significance of hierarchical multi-body potentials based on Delaunay tessellation and their application in sequence-structure alignment. Protein Sci, 6(7): 1467-1481, 1997.
34. A. Okabe, B. Boots, and K. Sugihara. Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. John Wiley & Sons, Chichester, UK, 1992.
35. P. A. Ramos. Computing roundness is easy if the set is almost round. In Proc. 15th Annu. ACM Sympos. Comput. Geom., pages 307-315, 1999.
36. F. M. Richards. The interpretation of protein structures: total volume, group volume distributions, and packing density. J. Molecular Biology, 82:1-14, 1974.
37. T. Rivlin. Approximation by circles. Computing, 21:93-104, 1979.
38. U. Roy and X. Zhang. Establishment of a pair of concentric circles with the minimum radial separation for assessing roundness errors. Computer Aided Design, 24(3): 161-168, 1992.
39. K. T. Simons, C. Kooperberg, E. Huang, and D. Baker. Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and Bayesian scoring functions. Journal of Molecular Biology, 268:209-225, 1997.
40. R. Singh, A. Tropsha, and I. Vaisman. Delaunay tessellation of proteins. J. Comput. Biol., 3:213-222, 1996.
41. M. Smid and R. Janardan. On the width and roundness of a set of points in the plane. In Canadian Conference on Computational Geometry, pages 193-198, Aug. 1995.
42. J. Tsai and M. Gerstein. Calculations of protein volumes: sensitivity analysis and parameter database. Bioinformatics, 18:985-995, 2002.
43. J. Tsai, R. Taylor, C. Chothia, and M. Gerstein. The packing density in proteins: Standard radii and volumes. Journal of Molecular Biology, 290(1):253-266, 1999.
44. G. M. Voronoi. Nouvelles applications des paramètres continus à la théorie des formes quadratiques, deuxième Mémoire: Recherches sur les parallélloèdres primitifs. J. Reine Angew. Math., 134:198-287, 1908.
45. H. Wako and T. Yamato. Novel method to detect a motif of local structures in different protein conformations. Protein Engineering, 11:981-990, 1998.
46. G. Weberndorfer, I. L. Hofacker, and P. F. Stadler. An efficient potential for protein sequence design. In Computer Science in Biology. Univ. Bielefeld, D. GCB '99 Proceedings, pages 107-112, Hannover, Germany, 1999. http://www.tbi.univie.ac.at/papers/Abstracts/GCB026.ps.gz.
47. L. Wernisch, M. Hunting, and S. Wodak. Identification of structural domains in proteins by a graph heuristic. Proteins, 35(3):338-352, 1999.
48. R. Zimmer. M. Wöhler, and R. Thiele. New scoring schemes for protein fold recognition based on Voronoi contacts. Bioinformatics, 14(3):295-308, 1998.