Testing of clustering

SIAM Journal on Discrete Mathematics

Volumn 16, Issue 3, 2003, Pages 393-417

  Alon, Noga ^a   Dar, Seannie ^b   Parnas, Michal ^b   Ron, Dana ^a  

^a TEL AVIV UNIVERSITY   (Israel)

^b ACADEMIC COLLEGE OF TEL AVIV YAFFO   (Israel)

Author keywords

Approximation algorithms; Clustering; Property testing; Randomized algorithms

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; POLYNOMIALS; PROBLEM SOLVING;

CLUSTERING; PROPERTY TESTING;

SET THEORY;

EID: 0041384098     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480102410973     Document Type: Article

References (48)

1. P. K. Agrawal and C. M. Procopiuc, Exact and approximation algorithms for clustering, Algorithmica, 33 (2002), pp. 201-226.
2. P. K. Agrawal and M. Sharir, Efficient algorithms for geometric optimization, ACM Comput. Surveys, 30 (1998), pp. 412-458.
3. P. K. Agrawal, M. Sharir, and S. Toledo, An Efficient Multi-dimensional Searching Technique and Its Applications, Technical Report CS-1993-20, Department of Computer Science, Duke University, Durham, NC, 1993.
4. N. Alon, E. Fischer, M. Krivelevich, and M Szegedy, Efficient testing of large graphs, Combinatorica, 20 (2000), pp. 451-476.
5. N. Alon and M. Krivelevich, Testing k-colorability, SIAM J. Discrete Math., 15 (2002), pp. 211-227.
6. N. Alon, M. Krivelevich, I. Newman, and M Szegedy, Regular languages are testable with a constant number of queries, SIAM J. Comput., 30 (2001), pp. 1842-1862.
7. M. R. Anderberg, Cluster Analysis for Applications, Academic Press, New York, 1973.
8. M. Bender and D. Ron, Testing properties of directed graphs: Acyclicity and connectivity, Random Structures Algorithms, 20 (2002), pp. 184-205.
9. M. Blum, M. Luby, and R. Rubinfeld, Self-testing/correcting with applications to numerical problems, J. Assoc. Comput. Mach., 47 (1993), pp. 549-595.
10. B. Chazelle and J. Matoušek, On linear-time deterministic algorithms for optimization problems in fixed dimension, J. Algorithms, 21 (1996), pp. 579-597.
11. A. Czumaj and C. Sohler, Combinatorial programs and efficient property testers, in Proceedings of 43rd Annual Symposium on Foundations of Computer Science, IEEE, Los Alamitos, CA, 2002, pp. 83-92.
12. A. Czumaj, C. Sohler, and M. Ziegler, Property testing in computational geometry, in Proceedings of the 8th ESA, Lecture Notes in Comput. Sci. 1879, M. Paterson, ed., Springer-Verlag, Berlin, 2000, pp. 155-166.
13. Y. Dodis, O. Goldreich, E. Lehman, S. Raskhodnikova, D. Ron, and A. Samorodnitsky, Improved testing algorithms for monotonicity, in Proceedings of RANDOM, Lecture Notes in Comput. Sci. 1671, Springer-Verlag, Berlin, 1999, pp. 97-108.
14. D. Hochbaum, ed., Approximation Algorithms for NP-Hard Problems, PWS Publishing Company, Boston, 1997.
15. Z. Drezner, ed., Facility Location, Springer-Verlag, New York, 1995.
16. F. Ergun, S. Kannan, S. R. Kumar, R. Rubinfeld, and M. Viswanathan, Spot-checkers, J. Comput. System Sci., 60 (2000), pp. 717-751.
17. T. Feder and D. H. Greene, Optimal algorithms for approximate clustering, in Proceedings of 20th Annual Symposium on Theory of Computing, ACM, New York, 1988, pp. 434-444.
18. E. Fischer, The art of uninformed decisions: A primer to property testing, Bull. Eur. Assoc. Theor. Comput. Sci. EATCS, 75 (2001), pp. 97-126.
19. R. J. Fowler, M. S. Paterson, and S. L. Tanimoto, Optimal packing and covering in the plane are NP-complete, Inform. Process. Lett., 12 (1981), pp. 133-137.
20. A. Frieze and R. Kanan, Quick approximation to matrices and applications, Combinatorica, 19 (1999), pp. 175-220.
21. O. Goldreich, S. Goldwasser, E. Lehman, D. Ron, and A. Samordinsky, Testing monotonicity, Combinatorica, 20 (2000), pp. 301-337.
22. O. Goldreich, S. Goldwasser, and D. Ron, Property testing and its connection to learning and approximation, J. Assoc. Comput. Mach., 45 (1998), pp. 653-750.
23. O. Goldreich and D. Ron, A sublinear bipartiteness tester for bounded degree graphs, Combinatorica, 19 (1999), pp. 335-373.
24. O. Goldreich and D. Ron, Property testing in bounded degree graphs, Algorithmica, 32 (2002), pp. 302-343.
25. T. Gonzalez, Clustering to minimize the maximum intercluster distance, Theoret. Comput. Sci., 38 (1985), pp. 293-306.
26. J. Hamkins and K. Zeger, Asymptotically dense spherical codes-part i: Wrapped spherical codes, IEEE Trans. Inform. Theory, 43 (1997), pp. 1774-1785.
27. D. Haussler and E. Welzl, ε-nets and simplex range queries, Discrete Comput. Geom., 2 (1987), pp. 127-151.
28. D. Hochbaum and D. Shmoys, A best possible heuristic for the k-center problem, Math. Oper. Res., 10 (1985), pp. 180-184.
29. D. Hochbaum and D. Shmoys, A unified approach to approximation algorithms for bottleneck problems, J. Assoc. Comput. Mach., 33 (1986), pp. 533-550.
30. A. K. Jain and R. C. Dubes, Algorithms for Clustering, Prentice-Hall, Englewood Cliffs, NJ, 1988.
31. J. Jolion, P. Meer, and S. Batauche, Robust clustering with applications in computer vision, IEEE Trans. Pattern Analysis Mach. Intell., 13 (1991), pp. 791-802.
32. L. Kaufman and P. J. Rousseuw, Finding Groups in Data: An Introduction to Cluster Analysis, John Wiley, New York, 1990.
33. M. Kearns and D. Ron, Testing problems with sub-learning sample complexity, J. Comput. System Sci., 61 (2001), pp. 428-456.
34. R. Lupton, F. M. Maley, and N. Young, Data collection for the Sloan digital sky survey-a network-flow heuristic, J. Algorithms, 27 (1998), pp. 339-356.
35. N. Megiddo, Linear programming in linear time when the dimension is fixed, J. Assoc. Comput. Mach., 31 (1984), pp. 114-127.
36. N. Megiddo and E. Zemel, An o(n log n) randomizing algorithm for the weighted Euclidean 1-center problem, J. Algorithms, 7 (1986), pp. 358-368.
37. N. Mishra, D. Oblinger, and L. Pitt, Sublinear time approximate clustering, in Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 2001, pp. 439-447.
38. R. Motwani and P. Raghavan, Randomized Algorithms, Cambridge University Press, Cambridge, UK, 1995.
39. M. Parnas and D. Ron, Testing the diameter of graphs, Random Structures Algorithms, 20 (2002), pp. 165-183.
40. C. M. Procopiuc, Clustering Problems and Their Applications (A Survey), http://www.cs.duke.edu/~magda (2000).
41. P. Raghavan, Information retrieval algorithms: A survey, in Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, 1997, pp. 11-18.
42. E. A. Ramos, Deterministic algorithms for 3-d diameter and some 2-d lower envelopes, in Proceedings of the 16th Symposium on Computational Geometry, ACM, New York, 2000, pp. 290-299.
43. D. Ron, Property testing, in Handbook of Randomized Computing, Vol. II, in Handbook of Randomized Computing, S. Rajasekaran, P. Pardalos, J. Reif, and J. Rolim, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001, pp. 597-649.
44. R. Rubinfeld, On the robustness of functional equations, SIAM J. Comput., 28 (1999), pp. 1972-1997.
45. R. Rubinfeld and M. Sudan, Robust characterizations of polynomials with applications to program testing, SIAM J. Comput., 25 (1996), pp. 252-271.
46. L. Schulman, Private communication, 2000.
47. J. Shafer, R. Agrawal, and M. Mehta, Sprint: A scalable parallel classifier for data mining, in Proceedings of 22nd International Conference on Very Large Databases, Morgan Kaufmann, San Francisco, 1996, pp. 544-555.
48. V. N. Vapnik and A. Ya. Chervonenkis, On the uniform convergence of relative frequencies of events to their probabilities, Theory Probab. Appl., 16 (1971), pp. 264-280.