Geometric clustering: Fixed-parameter tractability and lower bounds with respect to the dimension

ACM Transactions on Algorithms

Volumn 7, Issue 4, 2011, Pages

  Cabello, Sergio ^a   Giannopoulos, Panos ^b   Knauer, Christian ^c   Marx, Dániel ^d   Rote, Günter ^c  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

^b HUMBOLDT UNIVERSITY   (Germany)

^c FREIE UNIVERSITÄT BERLIN   (Germany)

^d BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

Clustering; Complexity; Dimension; Fixed parameter tractability; Lower bound

Indexed keywords

CLUSTERING; COMPLEXITY; DIMENSION; FIXED-PARAMETER TRACTABILITY; LOWER BOUNDS;

ALGORITHMS;

EID: 80053468956     PISSN: 15496325     EISSN: 15496333     Source Type: Journal    
DOI: 10.1145/2000807.2000811     Document Type: Article

References (23)

1. AGARWAL, P. K. AND SHARIR, M. 1998. Efficient algorithms for geometric optimization. ACM Comput. Surv. 30, 412-458.
2. ASSA, E. AND KATZ, M. J. 1999. 3-piercing of d-dimensional boxes and homothetic triangles. Int. J. Comput. Geometry Appl. 9, 3, 249-260.
3. CABELLO, S., GIANNOPOULOS, P., KNAUER, C., AND ROTE, G. 2008. Geometric clustering: fixed-parameter tractabil-ity and lower bounds with respect to the dimension. In Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). 836-843.
4. CHAN, T. M. 1999a. Geometric applications of a randomized optimization technique. Disc. Computat. Geom. 22, 4, 547-567.
5. CHAN, T. M. 1999b. More planar two-center algorithms. Comput. Geom. Theory Appl. 13, 3, 189-198. (Pubitemid 129550154)
6. CHEN, J., CHOR, B., FELLOWS, M., HUANG, X., JUEDES, D., KANJ, I. A., AND XIA, G. 2005. Tight lower bounds for certain parameterized NP-hard problems. Inf. Computat. 201, 2, 216-231. (Pubitemid 41240616)
7. CHEN, J., HUANG, X., KANJ, I. A., AND XIA, G. 2004. Linear FPT reductions and computational lower bounds. In Proceedings of the 36th Annual ACM Symposium on Theory of Computing. ACM, New York, 212-221.
8. DEMAINE, E. D., FOMIN, F. V., HAJIAGHAYI, M., AND THILIKOS, D. M. 2005. Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs. ACM Trans. Algor. 1, 1, 33-47.
9. DOWNEY, R. AND FELLOWS, M. 1999. Parameterized Complexity. Springer-Verlag
10. DREZNER, Z., Ed. 1995. Facility Location: A Survey of Applications and Methods. Springer-Verlag.
11. EPPSTEIN, D. 1997. Fast construction of planar two-centers. In Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). 131-138.
12. FLUM, J. AND GROHE, M. 2006. Parameterized Complexity Theory. Texts in Theoretical Computer Science, vol. XIV. Springer-Verlag.
13. FOWLER, R. J., PATERSON, M. S., AND TANIMOTO, S. L. 1981. Optimal packing and covering in the plane are NP-complete. Inf. Proc. Lett. 12, 3, 133-137.
14. FREDERICKSON, G. N. AND JOHNSON, D. B. 1984. Generalized selection and ranking: Sorted matrices. SIAM J. Comput. 13, 14-30.
15. HOFFMANN, M. 2001. Covering polygons with few rectangles. In Abstracts of the 17th European Workshop on Computational Geometry (EuroCG'01). 39-42.
16. HOFFMANN, M. 2002. A matrix search algorithm with applications to rectilinear 3-centers of polygons. Personal communication.
17. IMPAGLIAZZO, R., PATURI, R., AND ZANE, F. 2001. Which problems have strongly exponential complexity? J. Comput. System Sci. 63, 4, 512-530. (Special issue on FOCS'98). (Pubitemid 34325767)
18. MARX, D. 2005. Efficient approximation schemes for geometric problems? In Proceedings of the 13th Annual European Symposium on Algorithms (ESA). Lecture Notes in Computer Science, vol. 3669. Springer-Verlag, 448-459. (Pubitemid 41491547)
19. MEGIDDO, N. 1990. On the complexity of some geometric problems in unbounded dimension. J. Symb. Comput. 10, 3-4, 327-334.
20. MEGIDDO, N. AND SUPOWIT, K. J. 1984. On the complexity of some common geometric location problems. SIAM J. Comput. 1 3, 182-196. (Pubitemid 15494582)
21. NUSSBAUM, D. 1997. Rectilinear p-piercing problems. In Proceedings of the Annual International Symposium on Symbolic and Algebraic Computation. ACM, 316-323.
22. SEGAL, M. 1999. On piercing sets of axis-parallel rectangles and rings. Int. J. Comput. Geom. Appl. 9, 3, 219-234.
23. SHARIR, M. AND WELZL, E. 1996. Rectilinear and polygonal p-piercing and p-center problems. In Proceedings of the 12th Annual Symposium on Computational Geometry. ACM Press, 122-132.