Approximation algorithms for clustering to minimize the sum of diameters

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

Volumn 1851, Issue , 2000, Pages 237-250

  Doddi, Srinivas R ^a   Marathe, Madhav V ^a   Ravi, S S ^b   Taylor, David Scot ^c   Widmayer, Peter ^d  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b State University of New York   (United States)

^c University of California   (United States)

^d ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION ALGORITHMS; GRAPH THEORY; OPTIMAL SYSTEMS; OPTIMIZATION; POLYNOMIAL APPROXIMATION; TREES (MATHEMATICS);

COMPLETE GRAPHS; EDGE-WEIGHTED GRAPH; NUMBER OF CLUSTERS; PERFORMANCE GUARANTEES; POLYNOMIAL-TIME ALGORITHMS; SUM-OF-DIAMETERS; TRIANGLE INEQUALITY; UNDERLYING GRAPHS;

CLUSTERING ALGORITHMS;

EID: 84956862930     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44985-X     Document Type: Conference Paper

References (29)

1. B. Awerbuch, B. Berger, L. Cowen and D. Peleg, “Near-Linear Time Construction of Sparse Neighborhood Covers", SIAM J. Computing, Vol. 28, No. 1, 1998, pp. 263-277.
2. P. K. Agarwal and C. M. Procopiuc, “Exact and Approximate Algorithms for Clustering", Proc. 9th ACM-SIAM Symposium on Discrete Algorithms (SODA'98), San Francisco, CA, Jan. 1998, pp. 658-667.
3. P. K. Agarwal and C. M. Procopiuc, “Approximation Algorithms for Projective Clustering", Proc. 11th ACM-SIAM Symposium on Discrete Algorithms (SODA'2000), San Francisco, CA, Jan. 2000, pp. 538-547.
4. V. Batagelj, S. Korenjak-Cerne and S. Klavzar, “Dynamic Programming and Convex Clustering", Algorithmica, Vol. 11, No. 2, Feb. 1994, pp. 93-103.
5. P. Brucker, “On the Complexity of Clustering Problems", in Optimization and Operations Research, Lecture Notes in Economics and Mathematical Systems, Vol. 157, Edited by M. Beckmann and H. Kunzi, Springer-Verlag, Heidelberg, 1978, pp. 45-54.
6. M. Charikar, C. Chekuri, T. Feder and R. Motwani, “Incremental Clustering and Dynamic Information Retrieval", Proc. 29th Annual ACM Symposium on Theory of Computing (STOC'97), El Paso, TX, May 1997, pp. 626-634.
7. V. Capoyleas, G. Rote and G. Woeginger, “Geometric Clusterings", J. Algorithms, Vol. 12, No. 2, Jun. 1991, pp. 341-356.
8. A. Datta, “Efficient Parallel Algorithms for Geometric k-Clustering Problems", Proc. 11th Annual Symposium on Theoretical Aspects of Computer Science (STACS'94), Caen, France, Feb. 1994, Springer-Verlag Lecture Notes in Computer Science, Vol. 775, pp. 475-486.
9. R. Duda and P. Hart, Pattern Classification and Scene Analysis, Wiley-Interscience, New York, NY, 1973.
10. J. S. Deogan, D. Kratsch and G. Steiner, “An Approximation Algorithm for Clustering Graphs with a Dominating Diametral Path", Information Processing Letters, Vol. 61, No. 3, Feb. 1997, pp. 121-127.
11. T. Feder and D. H. Greene, “Optimal Algorithms for Approximate Clustering", Proc. 20th Annual ACM Symposium on Theory of Computing (STOC'88), Chicago, IL, May 1988, pp. 434-444.
12. R. Fowler, M. Paterson and S. Tanimoto, “Optimal Packing and Covering in the Plane", Information Processing Letters, Vol. 12, 1981, pp. 133-137.
13. N. Guttmann-Beck and R. Hassin, “Approximation Algorithms for Min-sum p-Clustering", Discrete Applied Mathematics, Vol. 89, 1998, pp. 125-142.
14. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness, W. H. Freeman and Co., San Francisco, CA, 1979.
15. T. F. Gonzalez, “Clustering to Minimize the Maximum Intercluster Distance", Theoretical Computer Science, Vol. 38, No. 2-3, Jun. 1985, pp. 293-306.
16. P. Hansen and B. Jaumard, “Minimum Sum of Diameters Clustering," Journal of Classification, Vol. 4, 1987, pp. 215-226.
17. P. Hansen and B. Jaumard, “Cluster Analysis and Mathematical Programming, Mathematical Programming, Vol. 79, Aug. 1997, pp. 191-215.
18. D. S. Hochbaum (Editor), Approximation Algorithms for NP-Hard Problems, PWS Publishing Company, Boston, MA, 1997.
19. D. S. Hochbaum and D. B. Shmoys, “A Unified Approach to Approximation Algorithms for Bottleneck Problems", J. ACM, Vol. 33, No. 3, July 1986, pp. 533-550.
20. A. Jain and R. Dubes, Algorithms for Clustering Data, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1988.
21. S. Khuller, A. Moss and J. Naor, “The Budgeted Maximum Coverage Problem", Information Processing Letters, Vol. 70, 1999, pp. 39-45.
22. J. Matousek, “On Approximate Geometric k-Clustering", Manuscript, Department of Applied Mathematics, Charles University, Prague, Czech Republic, 1999.
23. M. V. Marathe, R. Ravi, R. Sundaram, S. S. Ravi, D. J. Rosenkrantz and H. B. Hunt III, “Bicriteria Network Design Problems", J. Algorithms, Vol. 28, No. 1, July 1998, pp. 142-171.
24. N. Meggiddo and K. J. Supowit, “On the complexity of some common geometric location problems," SIAM J. Computing, Vol. 13, 1984, pp. 182-196.
25. C. L. Monma and S. Suri, “Partitioning Points and Graphs to Minimize the Maximum or the Sum of Diameters", Proc. 6th Int. Conf. Theory and Applications of Graphs, Kalamazoo, Michigan, May 1989.
26. J. Plesník, “Complexity of Decomposing Graphs into Factors with Given Diameters or Radii", Math. Slovaca, Vol. 32, No. 4, 1982, pp. 379-388.
27. U. Pferschy, R. Rudolf and G. J. Woeginger, “Some Geometric Clustering Problems", Nordic J. Computing, Vol. 1, No. 2, Summer 1994, pp. 246-263.
28. P. Raghavan, “Information Retrieval Algorithms: A Survey", Proc. 8th ACM-SIAM Symposium on Discrete Algorithms (SODA'97), Jan. 1997, pp. 11-18.
29. T. Zhang, R. Ramakrishnan and M. Livny, “Birch: An Efficient Data Clustering Method for Very Large Databases", Proc. ACM-SIGMOD International Conference on Management of Data (SIGMOD'96), Aug. 1996, pp. 103-114.