Counting distance permutations

Journal of Discrete Algorithms

Volumn 7, Issue 1, 2009, Pages 49-61

  Skala, Matthew ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Distance permutation; Metric space; Nearest neighbour; Voronoi diagram

Indexed keywords

AUTOMATIC INDEXING; SET THEORY;

DISTANCE PERMUTATION; DOCUMENT DATABASES; METRIC SPACE; NEAREST NEIGHBOUR; PROXIMITY SEARCHING; REFERENCE SITES; STORAGE SPACES; TREE METRICS; VECTOR SPACES; VORONOI DIAGRAM;

TOPOLOGY;

EID: 58549104890     PISSN: 15708667     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jda.2008.09.011     Document Type: Article

References (31)

1. Agarwala R., Bafna V., Farach M., Narayanan B., Paterson M., and Thorup M. On the approximability of numerical taxonomy (fitting distances by tree metrics). Proceedings of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'96) (1996), ACM/SIAM, Atlanta, Georgia, USA
2. Alon N., Karp R.M., Peleg D., and West D.B. A graph-theoretic game and its application to the k-server problem. SIAM Journal on Computing 24 1 (1995) 78-100
3. Aurenhammer F. Voronoi diagrams-a survey of a fundamental geometric data structure. ACM Computing Surveys 23 3 (1991)
4. Bartal Y. Probabilistic approximations of metric spaces and its algorithmic applications. 37th Annual Symposium on Foundations of Computer Science (FOCS'96) (1996), IEEE
5. Björner A., Las Vergnas M., Sturmfels B., White N., and Ziegler G.M. Oriented Matroids. second ed. (1999), Cambridge University Press
6. Buneman P. A note on the metric properties of trees. Journal of Combinatorial Theory, Series B 17 (1974) 48-50
7. Chávez E., Figueroa K., and Navarro G. Proximity searching in high dimensional spaces with a proximity preserving order. In: Gelbukh A., de Álbornoz A., and Terashima-Marín H. (Eds). 4th Mexican International Conference on Artificial Intelligence (MICAI'05) (2005), Springer
8. E. Chávez, G. Navarro, Measuring the dimensionality of general metric spaces, Tech. Rep. TR/DCC-00-1, Department of Computer Science, University of Chile, 2000
9. In: Chávez E., and Navarro G. (Eds). Proceedings of the 1st International Workshop on Similarity Search and Applications (SISAP'08). Apr. 11-12, 2008 (2008), IEEE Computer Society, Cancún, Mexico
10. Dress A.W.M. Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: A note on combinatorial properties of metric spaces. Advances in Mathematics 53 3 (1984) 321-402
11. Figueroa K., Chávez E., Navarro G., and Paredes R. On the least cost for proximity searching in metric spaces. In: Àlvarez C., and Serna M. (Eds). Experimental and Efficient Algorithms: 5th International Workshop (WEA'06) (2006), Springer
12. Figueroa K., Navarro G., and Chávez E. Metric spaces library, online. http://www.sisap.org/?f=library Accessed November 24, 2007
13. Grünbaum B. Arrangements and Spreads. Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics vol. 10 (1971), American Mathematical Society, Providence
14. Icking C., Klein R., Lê N.-M., and Ma L. Convex distance functions in 3-space are different. Fundamenta Informaticae 22 4 (1995) 331-352
15. Icking C., Klein R., Lê N.-M., Ma L., and Santos F. On bisectors for convex distance functions in 3-space. 11th Canadian Conference on Computational Geometry (CCCG '99) (1999), University of British Columbia
16. Lowe D.G. Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision 60 2 (2004) 91-110
17. Lynn B., Prabhakaran M., and Sahai A. Positive results and techniques for obfuscation. In: Cachin C., and Camenisch J. (Eds). Advances in Cryptology: International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT'04) (2004), Springer, Interlaken, Switzerland
18. A. Mandel, Topology of oriented matroids, Ph.D. thesis, University of Waterloo, 1982
19. Matoušek J. On embedding trees into uniformly convex Banach spaces. Israel Journal of Mathematics 114 1 (1999) 221-237
20. Micó L., Oncina J., and Vidal E. A new version of the nearest-neighbour approximating and eliminating search algorithm (AESA) with linear preprocessing time and memory requirements. Pattern Recognition Letters 15 1 (1994) 9-17
21. Ott E. Chaos in Dynamical Systems. second ed. (2002), Cambridge University Press, Cambridge, UK
22. Paredes R., and Chávez E. Using the k-nearest neighbor graph for proximity searching in metric spaces. In: Consens M.P., and Navarro G. (Eds). String Processing and Information Retrieval, 12th International Conference (SPIRE'05) (2005), Springer
23. Price D.J. Some unusual series occurring in n-dimensional geometry. The Mathematical Gazette 30 (1946) 149-150
24. Sahlgren M. The word-space model. Ph.D. thesis, Stockholm University, 2006. http://www.sics.se/~mange/TheWordSpaceModel.pdf
25. Santos F. On Delaunay oriented matroids for convex distance functions. Discrete & Computational Geometry 16 2 (1996) 197-210
26. Skala M. Measuring the difficulty of distance-based indexing. In: Consens M.P., and Navarro G. (Eds). String Processing and Information Retrieval: 12th International Conference (SPIRE'05) (2005), Springer
27. M. Skala, Counting distance permutations, in: Chávez and Navarro [9], pp. 69-76
28. Skala M.A. Aspects of metric spaces in computation. Ph.D. thesis, University of Waterloo, 2008. http://ansuz.sooke.bc.ca/books/thesis.pdf
29. Uhlmann J.K. Satisfying general proximity/similarity queries with metric trees. Information Processing Letters 40 (1991) 175-179
30. Vidal Ruiz E. An algorithm for finding nearest neighbors in (approximately) constant time. Pattern Recognition Letters 4 (1986) 145-157
31. Yianilos P.N. Data structures and algorithms for nearest neighbor search in general metric spaces. Fourth Annual ACM/SIGACT-SIAM (1993), Symposium on Discrete Algorithms (SODA'93), ACM/SIAM