Dynamic connectivity: Connecting to networks and geometry

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2008, Pages 95-104

  Chan, Timothy M ^a   Pǎtra̧cu, Mihai ^b   Roditty, Liam ^c  

^a UNIVERSITY OF WATERLOO   (Canada)

^b MIT MEDIA LAB   (United States)

^c WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

AMORTIZED TIMES; D LINES; DYNAMIC SETS; FUNDAMENTAL PROBLEMS; GEOMETRIC OBJECTS; INSERTIONS AND DELETIONS; INTERSECTION GRAPHS; MATRIX MULTIPLICATIONS; OF SENSORS; PARALLEL LINES; SUBGRAPH; SUBLINEAR; TIME RANGES; TRANSMISSION RADIUSES; UNDIRECTED GRAPHS;

COMPUTER NETWORKS; COMPUTER PROGRAMMING LANGUAGES; COMPUTERS; DATA STRUCTURES; FIBER OPTIC CHEMICAL SENSORS; FILE ORGANIZATION; INTERSECTIONS; ROUTERS; SENSOR NETWORKS;

COMPUTATIONAL GEOMETRY;

EID: 57949083674     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2008.29     Document Type: Conference Paper

References (41)

1. Peyman Afshani and Timothy M. Chan. Dynamic connectivity for axis-parallel rectangles. In Proc. 14th European Symposium on Algorithms (ESA), pages 16-27, 2006.
2. Pankaj K. Agarwal and Jeff Erickson. Geometric range searching and its relatives. In B. Chazelle, J. E. Goodman, and R. Pollack, editors, Advances in Discrete and Computational Geometry, pages 1-56. American Mathematical Society, 1999.
3. Pankaj K. Agarwal and Jirí Matoušek. On range searching with semialgebraic sets. Discrete & Computational Geometry, 11:393-418, 1994. See also MFCS'92.
4. Pankaj K. Agarwal and Marc J. van Kreveld. Connected component and simple polygon intersection searching. Algorithmica, 15(6):626-660,1996. See also WADS'93.
5. Noga Alon, Raphael Yuster, and Uri Zwick. Finding and counting given length cycles. Algorithmica, 17(3):209-223, 1997. See also ESA'94.
6. Timothy M. Chan. Dynamic subgraph connectivity with geometric applications. In Proc 34th ACM Symposium on Theory of Computing (STOC), pages 7-13, 2002.
7. Timothy M. Chan. A dynamic data structure for 3-d convex hulls and 2-d nearest neighbor queries. In Proc 17th ACM/SIAM Symposium on Discrete Algorithms (SODA), pages 1196-1202, 2006.
8. Don Coppersmith and Shmuel Winograd. Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation, 9(3):251-280, 1990. See also STOC'87.
9. Camil Demetrescu and Giuseppe F. Italiano. A new approach to dynamic all pairs shortest paths. Journal of the ACM, 51(6):968-992, 2004. See also STOC'03.
10. 2) barrier. Journal of the ACM, 52(2):147-156, 2005.
11. See also FOCS'00.
12. David Eppstein. Dynamic Euclidean minimum spanning trees and extrema of binary functions. Discrete & Computational Geometry, 13:111-122, 1995.
13. David Eppstein. Testing bipartiteness of geometric graphs. In Proc. 15th ACM/SIAM Symposium on Discrete Algorithms (SODA), pages 853-861, 2004.
14. Greg N. Frederickson. Data structures for on-line updating of minimum, spanning trees, with applications. SIAM Journal on Computing, 14(4):781-798, 1985.
15. See also STOC'83.
16. Daniele Frigioni and Giuseppe F. Italiano. Dynamically switching vertices in planar graphs. Algorithmica, 28(1):76-103, 2000.
17. See also ESA'97.
18. Leonidas J. Guibas, John Hershberger, Subhash Suri, and Li Zhang. Kinetic connectivity for unit disks. Discrete & Computational Geometry, 25(4):591-610, 2001. See also SoCG'00.
19. Leonidas J. Guibas, M. H. Overmars, and Micha Sharir. Intersecting line segments, ray shooting, and other applications of geometric partitioning techniques. In Proc. 1st Scandinavian Workshop on Algorithm Theory (SWAT), pages 64-73, 1988.
20. Monika Rauch Henzinger and Valerie King. Randomized fully dynamic graph algorithms with polylogarithmic time per operation. Journal of the ACM, 46(4):502-516, 1999. See also STOC'95.
21. John Hershberger and Subhash Suri. Kinetic connectivity of rectangles. In Proc. 15th ACM Symposium on Computational Geometry (SoCG), pages 237-246, 1999.
22. John Hershberger and Subhash Suri. Simplified kinetic connectivity for rectangles and hypercubes. In Proc 12th ACM/SIAM Symposium on Discrete Algorithms (SODA), pages 158-167, 2001.
23. Jacob Holm, Kristian de Lichtenberg, and Mikkel Thorup. Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. Journal of the ACM, 48(4):723-760, 2001. See also STOC'98.
24. Xiaohan Huang and Victor Y. Pan. Fast rectangular matrix multiplication and applications. Journal of Complexity, 14(2):257-299, 1998.
25. Hiroshi Imai. Finding connected components of an intersection graph of squares in the Euclidean plane. Information Processing Letters, 15(3): 125-128, 1982.
26. Hiroshi Imai and Takao Asano. Finding the connected, components and a maximum clique of an intersection graph of rectangles in the plane. Journal of Algorithms, 4(4):310-323, 1983.
27. Alon Itai and Michael Rodeh. Finding a minimum circuit in a graph. SIAM Journal on Computing, 7(4):413-423, 1978. See also STOC'77.
28. Valerie King. Fully dynamic algorithms for maintaining allpairs shortest paths and transitive closure in digraphs. In Proc 40th IEEE Symposium on Foundations of Computer Science (FOCS), pages 81-91, 1999.
29. Valerie King and Garry Sagert. A fully dynamic algorithm for maintaining the transitive closure. Journal of Computer and System Sciences, 65(1):150-167, 2002. See also STOC99.
30. Mario Alberto López and Ramakrishna Thurimella. On computing connected, components of line segments. IEEE Transactions on Computers, 44(4):597-601, 1995.
31. Jirí Matoušek. Efficient partition trees. Discrete & Computational Geometry, 8:315-334, 1992. See also SoCG'91.
32. Jirí Matoušek. Range searching with efficient hierarchical cuttings. Discrete & Computational Geometry, 10(2): 157-182, 1993.
33. Mihai Pǎtraşcu and Erik D. Demaine. Logarithmic lower bounds in the cell-probe model. SIAM Journal on Computing, 35(4):932-963, 2006. See also SODA'04 and STOC'04.
34. Mihai Pǎtraşcu and Mikkel Thorup. Planning for fast connectivity updates. In Proc. 48th IEEE Symposium on Foundations of Computer Science (FOCS), pages 263-271, 2007.
35. Liam Roditty and Uri Zwick. A fully dynamic reachability algorithm for directed graphs with an almost linear update time. In Proc. 36th ACM Symposium on Theory of Computing (STOC), pages 184-191, 2004.
36. Piotr Sankowski. Dynamic transitive closure via dynamic matrix inverse. In Proc 45th IEEE Symposium on Foundations of Computer Science (FOCS), pages 509-517, 2004.
37. Mikkel Thorup. Near-optimal fully-dynamic graph connectivity. In Proc. 32nd ACM Symposium on Theory of Computing (STOC), pages 343-350, 2000.
38. Mikkel Thorup. Worst-case update times for fully-dynamic all-pairs shortest paths. In Proc. 37th ACM Symposium on Theory of Computing (STOC), pages 112-119, 2005.
39. Mikkel Thorup. Fully-dynamic min-cut. Combinatorica, 27(1):91-127, 2007. See also STOC'01.
40. Raphael Yuster and Uri Zwick. Detecting short directed cycles using rectangular matrix multiplication and dynamic programming. In Proc. 15th ACM/SIAM Symposium on Discrete Algorithms (SODA), pages 254-260, 2004.
41. Raphael Yuster and Uri Zwick. Fast sparse matrix multiplication. ACM Transactions on Algorithms, 1(1):2-13, 2005. See all ESA'04.