Squarepants in a tree: Sum of subtree clustering and hyperbolic pants decomposition

ACM Transactions on Algorithms

Volumn 5, Issue 3, 2009, Pages

  Eppstein, David ^a  

^a Irvine   (United States)

Author keywords

Approximation algorithm; Hierarchical clustering; Hyperbolic geometry; Minimum spanning tree; Pants decomposition; Sum of cluster sizes

Indexed keywords

HIERARCHICAL CLUSTERING; HYPERBOLIC GEOMETRY; MINIMUM SPANNING TREE; PANTS DECOMPOSITION; SUM OF CLUSTER SIZES;

APPROXIMATION ALGORITHMS; GRAPH THEORY; QUERY PROCESSING; SET THEORY; TOPOLOGY;

CLUSTERING ALGORITHMS;

EID: 68649088644     PISSN: 15496325     EISSN: 15496333     Source Type: Journal    
DOI: 10.1145/1541885.1541890     Document Type: Article

References (30)

1. AGARWAL, P. K., AND PROCOPIUC, C. M. 2003. Approximation algorithms for projective clustering. J. Algor 46, 2, 115-139.
2. AGARWAL, P. K., PROCOPIUC, C. M., AND VARADARAJAN, K. R. 2003. A (1+ψ)-approximationalgorithm for 2-line-center. Comput. Geom. Theory Appl. 26, 2, 119-129.
3. ALSTRUP, S., HOLM, J., AND THORUP, M. 2000. Maintaining center and median in dynamic trees. In Proceedings of the 7th Scandinavian Workshop Algorithm Theory (SWAT 00). Lecture Notes in Computer Science, vol. 1851. Springer-Verlag, 46-56.
4. ALURU, S., AND SEVILGEN, F.E. 1999. Dynamic compressed hyperoctrees with applicationto the N-body problem. In Proceedings of the 19th Conference on Foundation Software Technology and Theoretical Computer Science. Lecture Notes in Computer Science, vol. 1738. Springer-Verlag, 21-33.
5. AMENTA, N., BERN, M. W., AND EPPSTEIN, D. 1998. The crust and the β-skeleton: Combinatorial curve reconstruction. Graph. Models Image Process. 60/2, 2, 125-135.
6. BENTLEY, J.L., SLEATER, D.D., TARJAN, R. E., AND WEI, V.K. 1986. Alocally adaptive data compression scheme. Comm. ACM 29, 4, 320-330.
7. BERN, M. W. 1993. Approximate closest-point queries in high dimensions. Inf. Process. Lett. 45, 95-99.
8. BERN, M. W., EPPSTEIN, D., AND TENG, S.-H. 1993. Parallel construction of quadtrees and quality triangulations. In Proceedings of the 3rd Workshop on Algorithms and Data Structures (WADS'93). Lecture Notes in Computer Science, vol. 709. Springer-Verlag, 188-199.
9. BLUNDO, C., AND DE PRISCO, R. 1996. New bounds on the expected length of one-to-one codes. IEEE Trans. Inf. Theory IT-42, 246-250.
10. BORODIN, A., OSTROVSKY, R., AND RABANI, Y. 2004. Subquadratic approximation algorithms for clustering problems in high-dimensional spaces. Mach. Learn. 56, 153-167.
11. CLARKSON, K. L. 1983. Fast algorithms for the all nearest neighbors problem. In Proceedings of the 24th IEEE Symposium Foundations of Computer Science (FOCS'83), 226-232.
12. DASGUPTA, S. 2002. Performance guarantees for hierarchical clustering. In Proceedings of the 15th Conference on Computational Learning Theory (COLT'02). Lecture Notes in Computer Science, vol. 2375. Springer-Verlag, 351-363.
13. ELIAS, P. 1987. Interval and recency rank source coding: Two online adaptive variable-length schemes. IEEE Trans. Inf. Theory IT-33, 3-10.
14. EPPSTEIN, D. 1994. Approximating the minimum weight Steiner triangulation. Discrete Comput. Geom. 11, 2, 163-191.
15. EPPSTEIN, D. 2000. Fast hierarchical clustering and other applications of dynamic closest pairs. J. Exper. Algor. 5, 1, 1-23.
16. EPPSTEIN, D., GOODRICH, M. T., AND SUN, J.Z. 2005. The skip quadtree:Asimple dynamic data structure for multi-dimensional data. In Proceedings of the 21st Symposium on Computational Geometry. ACM, 296-305.
17. ERICKSON, J., AND COLIN DE VERDIÈRE, É. 2006. Tightening nonsimple paths and cycles on surfaces. In Proceedings of the 17th ACM-SIAM Symposium on Discrete Algorithms (SODA'06), 192-201.
18. FEDER, T., AND GREENE, D. H. 1988. Optimal algorithms for approximate clustering. In Proceedings of the 20th ACM Symposium on Theory of Computing (STOC'88), 434-444.
19. GAREY, M. R., AND JOHNSON, D. S. 1979. Computers and Intractibility: A Guide to the Theory of NP-Completeness. W. H. Freeman.
20. JOHNSON, S. C. 1967. Hierarchical clustering schemes. Psychometrika 32, 3, 241-254.
21. KIRKPATRICK, D. G., AND HELL, P. 1978. On the complexity of a generalized matching problem. In Proceedings of the 10th ACM Symposium on Theory of Computing (STOC'78), 240-245.
22. KRAUTHGAMER, R., AND LEE, J. R. 2006. Algorithms on negatively curved spaces. In Proceedings of the 47th IEEE Symposium on Foundations of Computer Science, 119-132.
23. LEUNG-YAN-CHEONG, S. K., AND COVER, T. M. 1978. Some equivalences between Shannon entropy and Kolmogorov complexity. IEEE Trans. Inf. Theory IT-24, 331-338.
24. POON, S.-H., AND THITE, S. 2006. Pants decomposition of the punctured plane. ACM Computing Research Repository, cs.CG/0602080.
25. RUPPERT, J. 1995. ADelaunay refinement algorithm for two-dimensional meshgeneration. J. Algor. 18, 3, 548-585.
26. SAITOU, N., AND NEI, M. 1987. The neighbor-joining method: A new method for reconstructing phylo-genetic trees. Molecular Biol. Evol. 4, 4, 406-425.
27. SHANNON, C. E. 1948. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379-423.
28. TEUFEL, E. 1991. A generalization of the isoperimetric inequality in the hyperbolic plane. Archiv der Mathematik 57, 5, 508-513.
29. WYNER, A. D. 1972. An upper bound on the entropy series. Inf. Contr. 20, 176-181.
30. ZUPAN, J. 1982. Clustering of Large Data Sets. Chemometrics Research Studies Series. Research Studies Press, Chichester.