Dynamic subgraph connectivity with geometric applications

SIAM Journal on Computing

Volumn 36, Issue 3, 2006, Pages 681-694

  Chan, Timothy M ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Computational geometry; Connectivity; Data structures; Dynamic graph algorithms

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; DATA STRUCTURES; GRAPH THEORY; MATRIX ALGEBRA; QUERY LANGUAGES;

DYNAMIC GRAPH ALGORITHMS; DYNAMIC SUBGRAPH CONNECTIVITY; MULTIPLICATION EXPONENTS; POLYLOGARITHMIC FACTORS;

PROBLEM SOLVING;

EID: 34250866917     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S009753970343912X     Document Type: Article

References (34)

1. P. K. AGARWAL, N. ALON, B. ARONOV, AND S. SURI, Can visibility graphs be represented compactly?, Discrete Comput. Geom., 12 (1994), pp.347-365.
2. P. K. AGARWAL AND J. ERICKSON, Geometric range searching and its relatives, in Advances in Discrete and Computational Geometry, B. Chazelle, J. E. Goodman, and R. Pollack, eds., AMS, Providence, RI, 1999, pp. 1-56.
3. P. K. AGARWAL AND M. VAN KREVELD, Polygon and connected component intersection searching, Algorithmica, 15 (1996), pp. 626-660.
4. N. ALON, R. YUSTER, AND U. ZWICK, Finding and counting given length cycles, Algorithmica, 17 (1997), pp. 209-223.
5. T. M. CHAN, A fully dynamic algorithm for planar width, Discrete Comput. Geom., 30 (2003), pp. 17-24.
6. T. M. CHAN, Semi-online maintenance of geometric optima and measures, SIAM J. Comput., 32 (2003), pp. 700-716.
7. D. COPPERSMITH AND S. WINOGRAD, Matrix multiplication via arithmetic progressions, J. Symbolic Comput., 9 (1990), pp. 251-280.
8. T. H. CORMEN, C. E. LEISERSON, R. L. RIVEST, AND C. STEIN, Introduction to Algorithms, 2nd ed., MIT Press, Cambridge, MA, 2001.
9. 2) barrier, J. ACM, 52 (2005), pp. 147-156.
10. D. DOBKIN AND S. SURI, Maintenance of geometric extrema, J. Assoc. Comput. Mach., 38 (1991), pp. 275-298.
11. H. EDELSBRUNNER AND H. A. MAURER, On the intersection of orthogonal objects, Inform. Process. Lett., 13 (1981), pp. 177-181.
12. D. EPPSTEIN, Dynamic Euclidean minimum spanning trees and extrema of binary functions, Discrete Comput. Geom., 13 (1995), pp. 111-122.
13. D. EPPSTEIN, Z. GALIL, G. F. ITALIANO, AND A. NISSENZWEIG, Sparsification: A technique for speeding up dynamic graph algorithms, J. ACM, 44 (1997), pp. 669-696.
14. T. FEDER AND R. MOTWANI, Clique partitions, graph compression and speeding up algorithms, J. Comput. System Sci., 51 (1995), pp. 261-272.
15. G. N. FREDERICKSON, Data structures for on-line updating of minimum spanning trees, with applications, SIAM J. Comput., 14 (1985), pp. 781-798.
16. D. FRIGIONI AND G. F. ITALIANO, Dynamically switching vertices in planar graphs, Algorithmica, 28 (2000), pp. 76-103.
17. M. R. HENZINGER AND V. KING, Randomized dynamic graph algorithms with polylogarithmic time per operation, J. ACM, 46 (1999), pp. 502-516.
18. M. R. HENZINGER AND V. KING, Maintaining minimum spanning forests in dynamic graphs, SIAM J. Comput., 31 (2001), pp. 364-374.
19. J. HERSHBERGER AND S. SURI, Kinetic connectivity of rectangles, in Proceedings of the Fifteenth Annual Symposium on Computational Geometry, Miami, PL, 1999, pp. 237-246.
20. J. HERSHBERGER AND S. SURI, Simplified kinetic connectivity for rectangles and hypercubes, in Proceedings of the Twelfth Annual Symposium on Discrete Algorithms, Washington, D.C., 2001, pp. 158-167.
21. 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 (2001), pp. 723-760.
22. X. HUANG AND V. Y. PAN, Fast rectangular matrix multiplication and applications, J. Complexity, 14 (1998), pp. 257-299.
23. 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 (1983), pp. 310-323.
24. S. KHANNA, R. MOTWANI, AND R. H. WILSON, On certificates and lookahead on dynamic graph problems, Algorithmica, 21 (1998), pp. 377-394.
25. M. A. LOPEZ AND R. THURIMELLA, On computing connected components of line segments, IEEE Trans. Comput., 44 (1995), pp. 597-601.
26. K. MEHLHORN, Data Structures and Algorithms 3: Multi-Dimensional Searching and Computational Geometry, Springer-Verlag, Heidelberg, 1984.
27. K. MULMULEY, Computational Geometry: An Introduction Through Randomized Algorithms, Prentice-Hall, Englewood Cliffs, NJ, 1994.
28. M. H. OVERMARS, The Design of Dynamic Data Structures, Lecture Notes in Comput. Sci. 156, Springer-Verlag, Berlin, 1983.
29. F. P. PREPARATA AND M. I. SHAMOS, Computational Geometry: An Introduction, Springer-Verlag, New York, 1985.
30. L. RODITTY AND U. ZWICK, Improved dynamic reachability algorithms for directed graphs, in Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science, Vancouver, BC, Canada, 2002, pp. 679-689.
31. M. THORUP, Decremental dynamic connectivity, J. Algorithms, 33 (1999), pp. 229-243.
32. M. THORUP, Near-optimal fully-dynamic graph connectivity, in Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, Portland, OR, 2000, pp. 343-350.
33. R. YUSTER AND U. ZWICK, Detecting short directed cycles using rectangular matrix multiplication and dynamic programming, in Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, LA, 2004, pp. 247-253.
34. R. YUSTER AND U. ZWICK, Fast sparse matrix multiplication, ACM Trans. Algorithms, 1 (2005), pp. 2-13.