Lower bounds on performance of metric tree indexing schemes for exact similarity search in high dimensions

Algorithmica

Volumn 66, Issue 2, 2013, Pages 310-328

  Pestov, Vladimir ^a  

^a UNIVERSITY OF OTTAWA   (Canada)

Author keywords

Algorithm performance; Algorithms and data structures; Indexing schemes; Similarity search; Vapnik Chernonenkis theory

Indexed keywords

ALGORITHM PERFORMANCE; ALGORITHMS AND DATA STRUCTURES; INDEXING SCHEME; SIMILARITY SEARCH; VAPNIK-CHERNONENKIS THEORY;

ALGORITHMS; ASYMPTOTIC ANALYSIS; FORESTRY; PROBABILITY DISTRIBUTIONS;

INDEXING (OF INFORMATION);

ALGORITHMS; FORESTRY; INDEXING; PROBABILITY;

EID: 84878549142     PISSN: 01784617     EISSN: 14320541     Source Type: Journal    
DOI: 10.1007/s00453-012-9638-2     Document Type: Article

References (43)

1. Andoni, A., Indyk, P., PCtrascu, M.: On the optimality of the dimensionality reduction method. In: Proc. 47th IEEE Symp. on Foundations of Computer Science, pp. 449-458 (2006) (Pubitemid 351175533)
2. Barkol, O., Rabani, Y.: Tighter lower bounds for nearest neighbor search and related problems in the cell probe model. In: Proc. 32nd ACM Symp. on the Theory of Computing, pp. 388-396 (2000)
3. Beyer, K., Goldstein, J., Ramakrishnan, R., Shaft, U.: When is "nearest neighbor" meaningful. In: Proc. 7-th Intern. Conf. on Database Theory, ICDT-99, Jerusalem, pp. 217-235 (1999)
4. Borodin, A., Ostrovsky, R., Rabani, Y.: Lower bounds for high-dimensional nearest neighbor search and related problems. In: Proc. 31st Annual ACS Sympos. Theory Comput, pp. 312-321 (1999)
5. Bustos, B., Navarro, G., Chávez, E.: Pivot selection techniques for proximity searching in metric spaces. Pattern Recognit. Lett. 24, 2357-2366 (2003) (Pubitemid 36911079)
6. Chávez, E., Navarro, G.: A compact space decomposition for effective metric indexing. Pattern Recognit. Lett. 26, 1363-1376 (2005) (Pubitemid 40644699)
7. Chávez, E., Navarro, G., Baeza-Yates, R., Marroquín, J.L.: Searching in metric spaces. ACM Comput. Surv. 33, 273-321 (2001) (Pubitemid 33768485)
8. Ciaccia, P., Patella, M., Zezula, P.: M-tree: An efficient access method for similarity search in metric spaces. In: Proc. 23rd Int. Conf. on Very Large Data Bases, VLDB'97, Athens, Greece, pp. 426-435 (1997)
9. Ciaccia, P., Patella, M., Zezula, P.: A cost model for similarity queries in metric spaces. In: Proc. 17-th ACM Symposium on Principles of Database Systems, PODS'98, Seattle, WA, pp. 59-68 (1998)
10. Clarkson, K.L.: An algorithm for approximate closest-point queries. In: Proc. 10th Symp. Comp. Geom, pp. 160-164. Stony Brook, New York (1994)
11. Clarkson, K.L.: Nearest-neighbor searching and metric space dimensions. In: Nearest-Neighbor Methods for Learning and Vision: Theory and Practice, pp. 15-59. MIT Press, New York (2006)
12. Faragó, A., Linder, T., Lugosi, G.: Fast nearest neighbor search in dissimilarity spaces. IEEE Trans. Pattern Anal. Mach. Intell. 18, 957-962 (1993) (Pubitemid 23703599)
13. Goldberg, P.W., Jerrum, M.R.: Bounding the Vapnik-Chervonenkis dimension of concept classes parametrised by real numbers. Mach. Learn. 18, 131-148 (1995)
14. Hellerstein, J.M., Koutsoupias, E., Miranker, D.P., Papadimitriou, C., Samoladas, V.: On a model of indexability and its bounds for range queries. J. ACM 49(1), 35-55 (2002)
15. Indyk, P.: Nearest neighbours in high-dimensional spaces. In: Goodman, J.E., O'Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, pp. 877-892. Chapman and Hall/CRC, Boca Raton/London/New York/Washington, (2004)
16. Indyk, P., Motwani, R.: Approximate nearest neighbors: towards removing the curse of dimensionality. In: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, Dallas, Texas, pp. 604-613 (1998)
17. Katayama, N., Satoh, S.: The SR-tree: An index structure for high-dimensional nearest neighbour queries. In: Prof. 16-th Symposium on PODS, pp. 369-380 (1997) (Pubitemid 127456800)
18. Kushilevitz, E., Ostrovsky, R., Rabani, Y.: Efficient search for approximate nearest neighbor in high dimensional spaces. SIAM J. Comput. 30, 457-474 (2000)
19. Ledoux, M.: The Concentration of Measure Phenomenon. Mathematical Surveys and Monographs, vol. 89. American Mathematical Society, Providence (2001)
20. Milman, V.D., Schechtman, G.: Asymptotic Theory of Finite Dimensional Normed Spaces. Lecture Notes in Mathematics, vol. 1200. Springer, Berlin (1986)
21. Miltersen, P.B.: Cell probe complexity - a survey. In: 19th Conference on the Foundations of Software Technology and Theoretical Computer Science, FSTTCS (1999). Advances in Data Structures Workshop
22. Navarro, G.: Searching in metric spaces by spatial approximation. VLDB J. 11, 28-46 (2002) (Pubitemid 36156213)
23. Navarro, G.: Analysing metric space indexes: what for? Invited paper. In: Proc. 2nd Int. Workshop on Similarity Search and Applications, SISAP 2009, Prague, Czech Republic, pp. 3-10 (2009)
24. Navarro, G., Reyes, N.: Dynamic spatial approximation trees for massive data. In: Proc. 2nd Int. Workshop on Similarity Search and Applications, SISAP 2009, Prague, Czech Republic, pp. 81-88 (2009)
25. Panigrahy, R., Talwar, K., Wieder, U.: A geometric approach to lower bounds for approximate near-neighbor search and partial match. In: Proc. 49th IEEE Symp. on Foundations of Computer Science, pp. 414-423 (2008)
26. Panigrahy, R., Talwar, K., Wieder, U.: Lower bounds on near neighbor search via metric expansion. In: Foundations of Computer Science, FOCS, pp. 805-814 (2010)
27. PCtrascu, M., Thorup, M.: Higher lower bounds for near-neighbor and further rich problems. In: Proc. 47th IEEE Symp. on Foundations of Computer Science, pp. 646-654 (2006) (Pubitemid 351175552)
28. Pestov, V.: On the geometry of similarity search: dimensionality curse and concentration of measure. Inf. Process. Lett. 73, 47-51 (2000) (Pubitemid 30563374)
29. Pestov, V.: An axiomatic approach to intrinsic dimension of a dataset. Neural Netw. 21, 204-213 (2008)
30. Pestov, V.: Indexability, concentration, and VC theory. J. Discrete Algorithms (2012). doi: 10.1016/j.jda.2011.10.002
31. Pestov, V., Stojmirović, A.: Indexing schemes for similarity search: an illustrated paradigm. Fundam. Inform. 70, 367-385 (2006) (Pubitemid 43760897)
32. Samet, H.: Foundations of Multidimensional and Metric Data Structures. Morgan Kaufmann, San Francisco (2005)
33. Santini, S.: Exploratory Image Databases: Content-Based Retrieval. Academic Press, New York (2001)
34. Shaft, U., Ramakrishnan, R.: Theory of nearest neighbors indexability. ACM Trans. Database Syst. 31, 814-838 (2006) (Pubitemid 44600827)
35. Uhlmann, J.K.: Satisfying general proximity/similarity queries with metric trees. Inf. Process. Lett. 40, 175-179 (1991)
36. Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1998)
37. Vempala, S.S.: The Random Projection Method. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 65. American Mathematical Society, Providence (2004)
38. Vidyasagar, M.: Learning and Generalization, with Applications to Neural Networks, 2nd edn. Springer, London (2003)
39. Volnyansky, I., Pestov, V.: Curse of dimensionality in pivot-based indexes. In: Proc. 2nd Int. Workshop on Similarity Search and Applications, SISAP 2009, Prague, Czech Republic, pp. 39-46 (2009)
40. Weber, R., Schek, H.-J., Blott, S.: A quantatitive analysis and performance study for similarity-search methods in high-dimensional spaces. In: Proceedings of the 24-th VLDB Conference, New York, pp. 194-205 (1998)
41. White, D.A., Jain, R.: Similarity indexing with the SS-tree. In: Proc. 12th Conf. on Data Engineering, ICDE'96, La Jolla, CA, pp. 516-523 (1996)
42. Yianilos, P.: Data structures and algorithms for nearest neighbor search in general metric spaces. In: Proc. 3rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 311-321 (1993) (Pubitemid 23612715)
43. Zezula, P., Amato, G., Dohnal, Y., Batko, M.: Similarity Search. The Metric Space Approach. Springer, New York (2006)