Testing Bipartiteness of Geometric Intersection Graphs

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 15, Issue , 2004, Pages 853-861

  Eppstein, David ^a  

^a University of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DATA STRUCTURES; PROBLEM SOLVING; SET THEORY; TREES (MATHEMATICS);

BINARY SEARCHES; GRAPH CONNECTIVITY; HOPCROFT PROBLEMS;

COMPUTER SCIENCE;

EID: 1842486909     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (29)

1. P. K. Agarwal, H. Edelsbrunner, O. Schwarzkopf, and E. Welzl. Euclidean minimum spanning trees and brichromatic closest pairs. Discrete & Computatational Geometry 6:407-422, 1991.
2. P. K. Agarwal and J. Erickson. Geometric range searching and its relatives. Advances in Discrete and Computational Geometry, pp. 1-56. AMS, Contemporary Mathematics 223, 1999, http://compgeom.cs.uiuc.edu/~jeffe/pubs/ survey.html.
3. P. B. Callahan. The Well-Separated Pair Decomposition and its Applications. Ph.D. thesis, Johns Hopkins Univ., 1995.
4. T. M.-Y. Chan. Geometric applications of a randomized optimization technique. Discrete & Compuiatational Geometry 22(4): 547-567, December 1999.
5. B. Chazelle and H. Edelsbrunner. An optimal algorithm for intersecting line segments in the plane. J. ACM 39(1):1-54, 1992.
6. B. N. Clark, C. J. Colbourn, and D. S. Johnson. Unit disk graphs. Discrete Mathematics 86:165-177, 1990.
7. G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, 1999.
8. M. B. Dillencourt, D. Eppstein, and D. S. Hirschberg. Geometric thickness of complete graphs. J. Graph Algorithms & Applications 4(3):5-17, 2000, arXiv:math.CO/9910185.
9. D. Eppstein. Separating thickness from geometric thickness. Proc. 10th Int. Symp. Graph Drawing (GD'02), pp. 150-161. Springer-Verlag, Lecture Notes in Computer Science 2528, 2002, arXiv:math.CO/0204252.
10. D. Eppstein, Z. Galil, G. F. Italiano, and A. Nissenzweig. Sparsification - A technique for speeding up dynamic graph algorithms. J. ACM 44(5):669-696, September 1997.
11. D. Eppstein, G. L. Miller, and S.-H. Teng. A deterministic linear time algorithm for geometric separators and its applications. Fundamenta Informaticae 22(4):309-331, April 1995.
12. J. Erickson. New lower bounds for Hopcroft's problem. Discrete & Computatational Geometry 16(4):389-418, 1996, http://compgeom.cs.uiuc.edu/ ~jeffe/pubs/hopcroft.html.
13. M. R. Garey, D. S. Johnson, and L. Stockmeyer. Some simplified NP-complete graph problems. Theoretical Computer Science 1:237-267, 1976.
14. A. Graf, M. Stumpf, and G. Weißenfels. On coloring unit disk graphs. Algorithmica 20(3):277-293, 1998.
15. L. J. Guibas, J. E. Hershberger, S. Suri, and L. Zhang. Kinetic connectivity of unit disks. Discrete & Computatational Geometry 25(4):591-610, April 2001.
16. J. E. Hershberger and S. Suri. Kinetic connectivity of rectangles. Proc. 15th Symp. Computational Geometry, pp. 237-246. ACM, June 1999.
17. J. E. Hershberger and S. Suri. Simplified kinetic connectivity for rectangles and hypercubes. Proc. 12th Symp. Discrete Algorithms (SODA '01), pp. 158-167. ACM and SIAM, January 2001.
18. J. Holm, K. de Lichtenberg, and M. Thorup. Poly-logarithmic deterministic fully-dynamic graph algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. J. ACM 48(4):723-760, July 2001.
19. J. P. Hutchinson, T. Shermer, and A. Vince. On representation of some thickness-two graphs. Proc. 3rd Int. Symp. Graph Drawing (GD'95), pp. 324-332. Springer-Verlag, Lecture Notes in Computer Science 1027, September 1995.
20. H. Imai. Finding connected components of an intersection graph of squares in the Euclidean plane. Inform. Proc. Lett. 15(3):125-128, 1982.
21. H. Imai and T. Asano. Finding the connected components and a maximum clique of an intersection graph of rectangles in the plane. J. Algorithms 4:310-323, 1983.
22. P. C. Kainen. Thickness and coarseness of graphs. Abh. Math. Sem. Univ. Hamburg 39:88-95, 1973.
23. D. Krznaric and C. Levcopoulos. Minimum spanning trees in d dimensions. Proc. 5th Eur. Symp. Algorithms, pp. 341-349. Springer-Verlag, Lecture Notes in Computer Science 1248, September 1997.
24. A. Mansfield. Determining the thickness of a graph is NP-hard. Math. Proc. Cambridge Philos. Soc. 93(9):9-23, 1983.
25. G. L. Miller, S.-H. Teng, W. P. Thurston, and S. A. Vavasis. Separators for sphere-packings and nearest neighbor graphs. J. ACM 44(1):1-29, January 1997.
26. W. Schnyder. Embedding planar graphs on the grid. Proc. 1st Symp. Discrete Algorithms, pp. 138-148. ACM and SIAM, January 1990.
27. R. Tamassia and I. G. Tollis. Tesselation representations of planar graphs. Proc. 27th Allerton Conf. Commun. Control Comput., pp. 48-57, 1989.
28. S.-H. Teng. Points, spheres, and separators: a unified approach to graph partitioning. Ph.D. thesis, Carnegie-Mellon Univ., School of Computer Science, 1991.
29. D. R. Wood. Geometric thickness in a grid of linear area. Proc. Euroconf. Combinatorics, Graph Theory, and Applications, pp. 310-315. Univ. Autònoma de Barcelona, Centre de Recerca Matemàtica, September 2001, http://www.cs.usyd.edu.au/~davidw/papers/Wood-COMB01.ps.