A fixed-parameter approach to two-layer planarization

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

Volumn 2265 LNCS, Issue , 2002, Pages 1-15

  Dujmovic, V ^a   Fellows, M ^d   Hallett, M ^a   Kitching, M ^a   Liotta, Giuseppe ^b   McCartin, C ^e   Nishimura, N ^c   Ragde, P ^c   Rosamond, F ^d   Suderman, M ^a   Whitesides, S ^a   Wood, David R ^f  

^a MCGILL UNIVERSITY   (Canada)

^b UNIVERSITY OF PERUGIA   (Italy)

^c UNIVERSITY OF WATERLOO   (Canada)

^d UNIVERSITY OF VICTORIA   (Canada)

^e VICTORIA UNIVERSITY OF WELLINGTON   (New Zealand)

^f UNIVERSITY OF SYDNEY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

DRAWING (GRAPHICS);

BIPARTITE GRAPHS; EDGE CROSSING; FIXED-PARAMETER TRACTABILITY; LINEAR TIME; NP COMPLETE; PARALLEL LINE; PLANARIZATION; TWO-LAYER;

GRAPH THEORY;

EID: 84867480314     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45848-4_1     Document Type: Conference Paper

References (19)

1. G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Graph Drawing: Algorithms for the Visualization of Graphs. Prentice-Hall, 1999.
2. R. G. Downey and M. R. Fellows. Parametrized complexity. Springer, 1999.
3. V. Dujmović, M. Fellows, M. Hallett, M. Kitching, G. Liotta, C. McCartin, N. Nishimura, P. Ragde, F. Rosemand, M. Suderman, S. Whitesides, and D. R. Wood. On the parameterized complexity of layered graph drawing. In Proc. 9th European Symp. on Algorithms (ESA '01), to appear.
4. P. Eades, B. D. McKay, and N. C. Wormald. On an edge crossing problem. In Proc. 9th Australian Computer Science Conference, pages 327-334. Australian National University, 1986.
5. P. Eades and S. Whitesides. Drawing graphs in two layers. Theoret. Comput. Sci., 131(2):361-374, 1994.
6. P. Eades and N. C. Wormald. Edge crossings in drawings of bipartite graphs. Algorithmica, 11(4):379-403, 1994.
7. M. R. Garey and D. S. Johnson. Crossing number is NP-complete. SIAM J. Algebraic Discrete Methods, 4(3):312-316, 1983.
8. F. Harary and A. Schwenk. A new crossing number for bipartite graphs. Utilitas Math., 1:203-209, 1972.
9. M. Jünger and P. Mutzel. 2-layer straightline crossing minimization: performance of exact and heuristic algorithms. J. Graph Algorithms Appl., 1(1):1-25, 1997.
10. M. Kaufmann and D. Wagner, editors. Drawing Graphs: Methods and Models, volume 2025 of Lecture Notes in Comput. Sci. Springer, 2001.
11. T. Lengauer. Combinatorial Algorithms for Integrated Circuit Layout. Wiley, 1990.
12. P. Mutzel. An alternative method to crossing minimization on hierarchical graphs. SIAM J. Optimization, 11(4):1065-1080, 2001.
13. P. Mutzel. Optimization in leveled graphs. In P. M. Pardalos and C. A. Floudas, editors, Encyclopedia of Optimization. Kluwer, to appear.
14. P. Mutzel and R. Weiskircher. Two-layer planarization in graph drawing. In K. Y. Chwa and O. H. Ibarra, editors, Proc. 9th International Symp. on Algorithms and Computation (ISAAC'98), volume 1533 of Lecture Notes in Comput. Sci., pages 69-78. Springer, 1998.
15. F. Shahrokhi, O. Sýkora, L. A. Székely, and I. Vrťo. On bipartite drawings and the linear arrangement problem. SIAM J. Comput., 30(6):1773-1789, 2001.
16. K. Sugiyama, S. Tagawa, and M. Toda. Methods for visual understanding of hierarchical system structures. Trans. Systems Man Cybernet., 11(2):109-125, 1981.
17. N. Tomii, Y. Kambayashi, and S. Yajima. On planarization algorithms of 2-level graphs. Papers of tech. group on elect. comp., IECEJ, EC77-38:1-12, 1977.
18. V. Valls, R. Marti, and P. Lino. A branch and bound algorithm for minimizing the number of crossing arcs in bipartite graphs. J. Operat. Res., 90:303-319, 1996.
19. M. S. Waterman and J. R. Griggs. Interval graphs and maps of DNA. Bull. Math. Biol., 48(2):189-195, 1986.