Dynamic connectivity for axis-parallel rectangles

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

Volumn 4168 LNCS, Issue , 2006, Pages 16-27

  Afshani, Peyman ^a   Chan, Timothy M ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; COMPUTER GRAPHICS; MATRIX ALGEBRA; NUMERICAL METHODS;

INTERSECTION GRAPHS; QUERY TIME;

DATA STRUCTURES;

EID: 33750688193     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11841036_5     Document Type: Conference Paper

References (15)

1. P. K. Agarwal and J. Erickson. Geometric range searching and its relatives. In Advances in Discrete and Computational Geometry, pages 1-56. AMS Press, 1999.
2. T. M. Chan. Dynamic subgraph connectivity with geometric applications. In Proc. 34th ACM Sympos. on Theory of Comput., pages 7-13, 2002.
3. T. M. Chan. Semi-online maintenance of geometric optima and measures. SIAM J. Comput., 32:700-716, 2003.
4. K. L. Clarkson and P. W. Shor. Applications of random sampling in computational geometry, II. Discrete Comput. Geom., 4:387-421, 1989.
5. D. Coppersmith and S. Winograd. Matrix multiplication via arithmetic progressions. J. Symbolic Comput., 9:251-280, 1990.
6. H. Edelsbrunner and H. A. Maurer. On the intersection of orthogonal objects. Inform. Process. Lett., 13:177-181, 1981.
7. M. Fredman and M. Henzinger. Lower bounds for fully dynamic connectivity problems in graphs. Algorithmica, 22:351-362, 1998.
8. P. Gupta, R. Janardan, and M. Smid. Computational geometry: generalized intersection searching. In Handbook of Data Structures and Applications, pages 64-1-64-17. Chapman & Hall/CRC, Boca Raton, FL, 2005.
9. M. R. Henzinger and V. King. Randomized dynamic graph algorithms with polylogarithmic time per operation. J. ACM, 46:76-103, 2000.
10. J. Holm, K. de Lichtenberg, and M. Thorup. Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. J. ACM, 48:723-760, 2001.
11. H. Imai and T. Asano. Finding the connected components and a maximum clique of an intersection graph of rectangles in the plane. J. Algorithms, 4(4):310-323, 1983.
12. J. Matouašk. Lectures on Discrete Geometry. Springer-Verlag, 2002.
13. M. Pǎtraşcu and E. D. Demaine. Logarithmic lower bounds in the cell-probe model. SIAM J. Comput., 35(4):932r963, 2006.
14. M. Thorup. Decremental dynamic connectivity. J. Algorithms, 33(2):229-243, 1999.
15. M. Thorup. Near-optimal fully-dynamic graph connectivity. In Proc. 32nd ACM Sympos. on Theory of Comput., pages 343-350, 2000.