Practical construction of k-nearest neighbor graphs in metric spaces

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4007 LNCS, Issue , 2006, Pages 85-97

  Paredes, Rodrigo ^a   Chávez, Edgar ^b   Figueroa, Karina ^a,b   Navarro, Gonzalo ^a  

^a UNIVERSITY OF CHILE   (Chile)

^b UNIVERSIDAD MICHOACANA DE SAN NICOLÁS DE HIDALGO   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; COSTS; FUNCTIONS; MATRIX ALGEBRA; SET THEORY;

CONSTRUCTION ALGORITHMS; DISTANCE COMPUTATIONS; K-NEAREST NEIGHBOR GRAPH (KNNG);

GRAPH THEORY;

EID: 33746084482     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11764298_8     Document Type: Conference Paper

References (22)

1. S. Arya, D. Mount, N. Netanyahu, R. Silverman, and A. Wu. An optimal algorithm for approximate nearest neighbor searching in fixed dimension. In Proc. SODA'94, pages 573-583, 1994.
2. F. Aurenhammer. Voronoi diagrams - a survey of a fundamental geometric data structure. ACM Computing Surveys, 23(3), 1991.
3. R. Baeza-Yates, C. Hurtado, and M. Mendoza. Query clustering for boosting web page ranking. In Proc. AWIC'04, LNCS 3034, pages 164-175, 2004.
4. M. Brito, E. Chávez, A. Quiroz, and J. Yukich. Connectivity of the mutual k-nearest neighbor graph in clustering and outlier detection. Statistics & Probability Letters, 35:33-42, 1996.
5. P. Callahan. Optimal parallel all-nearest-neighbors using the well-separated pair decomposition. In Proc. FOCS'93, pages 332-340, 1993.
6. P. Callahan and R. Kosaraju. A decomposition of multidimensional point sets with applications to k nearest neighbors and n body potential Melds. JACM, 42(1):67-90, 1995.
7. E. Chávez and G. Navarro. A compact space decomposition for effective metric indexing. Pattern Recognition Letters, 26(9):1363-1376, 2005.
8. E. Chávez, G. Navarro, R. Baeza-Yates, and J.L. Marroquin. Searching in metric spaces. ACM Computing Surveys, 33(3):273-321, September 2001.
9. K. Clarkson. Fast algorithms for the all-nearest-neighbors problem. In Proc. FOCS'83, pages 226-232, 1983.
10. K. Clarkson. Nearest neighbor queries in metric spaces. Discrete Computational Geometry, 22(1):63-93, 1999.
11. M. Dickerson and D. Eppstein. Algorithms for proximity problems in higher dimensions. Computational Geometry Theory and Applications, 5:277-291, 1996.
12. R. Duda and P. Hart. Pattern Classification and Scene Analysis. Wiley, 1973.
13. H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag, 1987.
14. D. Eppstein and J. Erickson. Iterated nearest neighbors and finding minimal polytopes. Discrete & Computational Geometry, 11:321-350, 1994.
15. K. Figueroa. An efficient algorithm to all k nearest neighbor problem in metric spaces. Master's thesis, Universidad Michoacana, Mexico, 2000. In Spanish.
16. G. Hjaltason and H. Samet. Incremental similarity search in multimedia databases. Technical Report TR 4199, Dept. of Comp. Sci. Univ. of Maryland, Nov 2000.
17. I. Kalantari and G. McDonald. A data structure and an algorithm for the nearest point problem. IEEE Trans. Software Eng., 9(5):631-634, 1983.
18. D. R. Karger and M. Ruhl. Finding nearest neighbors in growth-restricted metrics. In Proc. STOC'02, pages 741-750, 2002.
19. R. Krauthgamer and J. Lee. Navigating nets: simple algorithms for proximity search. In Proc. SODA'04, pages 798-807, 2004.
20. R. Paredes and E. CháVez. Using the k-nearest neighbor graph for proximity searching in metric spaces. In Proc. SPIRE'05, LNCS 3772, pages 127-138, 2005.
21. R Development Core Team. R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria, 2004.
22. P. Vaidya. An O(n log n) algorithm for the all-nearest-neighbor problem. Discrete & Computational Geometry, 4:101-115, 1989.