Small space representations for metric min-sum k-clustering and their applications

Theory of Computing Systems

Volumn 46, Issue 3, 2010, Pages 416-442

  Czumaj, Artur ^a   Sohler, Christian ^b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Balanced k median; Clustering; Coresets; Min sum k clustering; Streaming algorithms; Sublinear space algorithms; Sublinear time algorithms

Indexed keywords

CLUSTERING; CORE SET; K-MEDIAN; MIN-SUM; STREAMING ALGORITHM; SUBLINEAR-TIME ALGORITHMS;

APPROXIMATION ALGORITHMS; OPTIMAL SYSTEMS; SET THEORY; TOPOLOGY;

CLUSTERING ALGORITHMS;

EID: 77951255269     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s00224-009-9235-1     Document Type: Article

References (44)

1. Abraham, I., Bartal, Y., Neiman, O.: Advances in metric embedding theory. In: Proc. 38th Annual ACM Symposium on Theory of Computing (STOC), pp. 271-286, 2006.
2. Alon, N., Dar, S., Parnas, M., Ron, D.: Testing of clustering. SIAM J. Discrete Math. 16(3), 393-417 (2003).
3. Agarwal, P. K., Har-Peled, S., Varadarajan, K. R.: Geometric approximation via coresets. In: Welzl, E. (ed.) Current Trends in Combinatorial and Computational Geometry. Cambridge University Press, New York (2005).
4. Bǎdoiu, M., Czumaj, A., Indyk, P., Sohler, C.: Facility location in sublinear time. In: Proc. 32nd Annual International Colloquium on Automata, Languages and Programming (ICALP), pp. 866-877, 2005.
5. Bǎdoiu, M., Har-Peled, S., Indyk, P.: Approximate clustering via core-sets. In: Proc. 34th Annual ACM Symposium on Theory of Computing (STOC), pp. 250-257, 2002.
6. Bartal, Y., Charikar, M., Raz, D.: Approximating min-sum k-clustering in metric spaces. In: Proc. 33rd Annual ACM Symposium on Theory of Computing (STOC), pp. 11-20, 2001.
7. Berkhin, P.: Survey of clustering data mining techniques. Technical Report, Accrue Software, San Jose, CA (2002).
8. Charikar, M., Chekuri, C., Feder, T., Motwani, R.: Incremental clustering and dynamic information retrieval. In: Proc. 29th Annual ACM Symposium on Theory of Computing (STOC), pp. 626-635, 1997.
9. Charikar, M., O'Callaghan, L., Panigrahy, R.: Better streaming algorithms for clustering problems. In: Proc. 35th Annual ACM Symposium on Theory of Computing (STOC), pp. 30-39, 2003.
10. Chen, K.: On k-median clustering in high dimensions. In: Proc. 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1177-1185, 2006.
11. Czumaj, A., Sohler, C.: Abstract combinatorial programs and efficient property testers. SIAM J. Comput. 34(3), 580-615 (2005).
12. Czumaj, A., Sohler, C.: Sublinear-time approximation for clustering via random sampling. Random Struct. Algorithms 30(1-2), 226-256 (2007).
13. Czumaj, A., Sohler, C.: Sublinear-time algorithms. Bull. EATCS 89, 23-47 (2006).
14. Fernandez de la Vega, W., Karpinski, M., Kenyon, C., Rabani, Y.: Approximation schemes for clustering problems. In: Proc. 35th Annual ACM Symposium on Theory of Computing (STOC), pp. 50-58, 2003.
15. Fernandez de la Vega, W., Kenyon, C.: A randomized approximation scheme for metric MAX-CUT. J. Comput. Syst. Sci. 63(4), 531-541 (2001).
16. Fotakis, D.: Memoryless facility location in one pass. In: Proc. 23rd Annual Symposium on Theoretical Aspects of Computer Science (STACS), pp. 608-620, 2006.
17. Frahling, G., Sohler, C.: Coresets in dynamic geometric data streams. In: Proc. 37th Annual ACM Symposium on Theory of Computing (STOC), pp. 209-217, 2005.
18. Goemans, M. X., Williamson, D. P.: Improved approximation algorithms for Maximum Cut and satisfiability problems using semidefinite programming. J. ACM 42, 1115-1145 (1995).
19. Goldreich, O., Goldwasser, S., Ron, D.: Property testing and its connection to learning and approximation. J. ACM 45(4), 653-750 (1998).
20. Guha, S., Mishra, N., Motwani, R., O'Callaghan, L.: Clustering data streams. In: Proc. 41st IEEE Symposium on Foundations of Computer Science (FOCS), pp. 359-366, 2000.
21. Gutmann-Beck, N., Hassin, R.: Approximation algorithms for min-sum p-clustering. Discrete Appl. Math. 89, 125-142 (1998).
22. Har-Peled, S.: Clustering motion. In: Proc. 42nd IEEE Symposium on Foundations of Computer Science (FOCS), pp. 84-93, 2001.
23. Har-Peled, S., Mazumdar, S.: Coresets for k-means and k-medians and their applications. In: Proc. 36th Annual ACM Symposium on Theory of Computing (STOC), pp. 291-300, 2004.
24. Har-Peled, S., Kushal, A.: Smaller coresets for k-median and k-means clustering. In: Proc. 21st Annual ACM Symposium on Computational Geometry (SoCG), pp. 126-134, 2005.
25. Har-Peled, S., Varadarajan, K.: Projective clustering in high dimensions using core-sets. In: Proc. 18th Annual ACM Symposium on Computational Geometry (SoCG), pp. 312-318, 2002.
26. Indyk, P.: Sublinear time algorithms for metric space problems. In: Proc. 31st Annual ACM Symposium on Theory of Computing (STOC), pp. 428-434, 1999.
27. Indyk, P.: High-dimensional computational geometry. PhD thesis, Stanford University (2000).
28. Indyk, P.: Algorithms for dynamic geometric problems over data streams. In: Proc. 36th Annual ACM Symposium on Theory of Computing (STOC), pp. 373-380, 2004.
29. Jain, A. K., Murty, M. N., Flynn, P. J.: Data clustering: a review. ACM Comput. Surv. 31(3), 264-323 (2003).
30. Korn, F., Muthukrishnan, S., Srivastava, D.: Reverse nearest neighbor aggregates over data streams. In: Proc. 28th International Conference on Very Large Data Bases (VLDB), pp. 814-825, 2002.
31. Kumar, A., Sabharwal, Y., Sen, S.: A simple linear time (1+ε)-approximation algorithm for k-means clustering in any dimensions. In: Proc. 45th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 454-462, 2004.
32. Kumar, A., Sabharwal, Y., Sen, S.: Linear time algorithms for clustering problems in any dimensions. In: Proc. 32nd Annual International Colloquium on Automata, Languages and Programming (ICALP), pp. 1374-1385, 2005.
33. Mettu, R., Plaxton, G.: Optimal time bounds for approximate clustering. Machine Learning 56(1-3), 35-60 (2004).
34. Meyerson, A.: Online facility location. In: Proc. 42nd IEEE Symposium on Foundations of Computer Science (FOCS), pp. 426-431, 2001.
35. Meyerson, A., O'Callaghan, L., Plotkin, S.: A k-median algorithm with running time independent of data size. Machine Learning 56(1-3), 61-87 (2004).
36. Mishra, N., Oblinger, D., Pitt, L.: Sublinear time approximate clustering. In: Proc. 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 439-447, 2001.
37. Muthukrishnan, S.: Data streams: algorithms and applications. Found. Trends Theor. Comput. Sci. 1(2) (2005).
38. Parnas, M., Ron, D., Rubinfeld, R.: Tolerant property testing and distance approximation. Electronic Colloquium on Computational Complexity (ECCC), Report No. 10 (2004).
39. 1. In: Proc. 35th Annual ACM Symposium on Theory of Computing (STOC), pp. 456-462, 2003.
40. Sahni, S., Gonzalez, T.: P-complete approximation problems. J. ACM 23, 555-566 (1976).
41. Schulman, L. J.: Clustering for edge-cost minimization. In: Proc. 32nd Annual ACM Symposium on Theory of Computing (STOC), pp. 547-555, 2000.
42. Thorup, M.: Quick k-median, k-center, and facility location for sparse graphs. SIAM J. Comput. 34(2), 405-432 (2005).
43. Tokuyama, T., Nakano, J.: Geometric algorithms for the minimum cost assignment problem. Random Struct. Algorithms 6(4), 393-406 (1995).
44. Xu, R., II Wunsch, D.: Survey of clustering algorithms. IEEE Trans. Neural Netw. 16(3), 645-678 (2005).