An efficient fixed parameter tractable algorithm for 1-sided crossing minimization

Algorithmica (New York)

Volumn 40, Issue 1, 2004, Pages 15-31

  Dujmovic, Vida ^a   Whitesides, Sue ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Fixed parameter tractability; FPT; Graph drawing; Layer crossing minimization; Layer drawings; Level drawings; NP completeness; Sided crossing minimization

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER SCIENCE; GRAPH THEORY; MATRIX ALGEBRA; OPTIMIZATION; PARAMETER ESTIMATION; POLYNOMIALS;

1-LAYER CROSSING MINIMIZATION; 1-SIDED CROSSING MINIMIZATION; 2-LAYER DRAWINGS; 2-LEVEL DRAWINGS; FIXED PARAMETER TRACTABILITY; FPT; GRAPH DRAWING; NP-COMPLETENESS;

ALGORITHMS;

EID: 21044434912     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00453-004-1093-2     Document Type: Article

References (25)

1. M. J. Carpano. Automatic display of hierarchized graphs for computer aided decision analysis. IEEE Trans. Systems Man Cybernet., 10(11):705-715, 1980.
2. C. Catarci. The assignment heuristic for crossing reduction. IEEE Trans. Systems Man Cybernet., 25(3), 1995.
3. T. Corman, R. Rivest C. Leiserson, and C. Stein. Introduction to Algorithms, second edition. MIT Press, Cambridge, MA, 2001.
4. C. Demetrescu and I. Finocchi. Break the right cycles and get the best drawing. In Proc. of the 2nd Workshop on Algorithm Engineering and Experiments (ALENEX '00), pages 171-172, 2000.
5. G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Graph Drawing: Algorithms for the Visualization of Graphs. Prentice-H all, Englewood Cliffs, NJ, 1999.
6. R. G. Downey and M. R. Fellows. Parametrized Complexity. Springer-Verlag, New York, 1999.
7. S. Dresbach. A new heuristic layout algorithm for directed acyclic graphs. In U. Derigs, A. Bachern, and A. B. A. Drexl, editors, Operations Research Proceedings (1994), pages 121-126, 1995.
8. 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. A fixed-parameter approach to two-layer planarization. In P. Mutzel, editor, Proc. Graph Drawing: 9th International Symposium (GD '01), volume 2265 of Lecture Notes in Computer Science, pages 1-15. Springer-Verlag, Berlin, 2001.
9. 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 Symposium on Algorithms (ESA 2001), volume 2161 of Lecture Notes in Computer Science, pages 488-499. Springer-Verlag, Berlin, 2001.
10. P. Eades and D. Kelly. Heuristics for drawing 2-layered networks. Ars Combin., 21(A):89-98, 1986.
11. P. Eades and S. Whitesides. Drawing graphs in two layers. Theoret. Comput. Sci., 131(2):361-374, 1994.
12. P. Eades and N. C. Wormald. Edge crossings in drawings of bipartite graphs. Algorithmica. 11(4):379-403, 1994.
13. S. Felsner, G. Liotta, and S. Wismath. Straight-line drawings on restricted integer grids in two and three dimensions. In P. Mutzel, editor, Proc. Graph Drawing: 9th International Symposium (GD '01), volume 2265 of Lecture Notes in Computer Science, pages 328-342. Springer-Verlag, Berlin, 2001.
14. M. R. Garey and D. S. Johnson. Crossing number is NP-complete. SIAM J. Algebraic Discrete Methods, 4(3):312-316, 1983.
15. M. Grohe. Computing crossing numbers in quadratic time. In Proc. 32nd Annual ACM Symposium on Theory of Computing (STOC '01), pages 231-236, 2001.
16. 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.
17. T. Lengauer. Combinatorial Algorithms for Integrated Circuit Layout. Wiley, New York. 1990.
18. X. Muñoz, U. Unger, and I. Vrťo. One sided crossing minimization is NP-hard for sparse graphs. In P. Mutzel, editor, Proc. Graph Drawing: 9th International Symposium (GD '01), volume 2265 of Lecture Notes in Computer Science, pages 115-123. Springer-Verlag, Berlin, 2001.
19. H. Nagamochi. An improved approximation to the one-sided bilayer drawing. In G. Liotta, editor, Proc. Graph Drawing: 11th International Symposium (GD '03), volume 2912 of Lecture Notes in Computer Science, pages 406-418. Springer-Verlag, Berlin, 2003.
20. M. Suderman and S. Whitesides. Experiments with the fixed-parameter approach for two-layer planarization. In G. Liotta, editor, Proc. Graph Drawing: 11th International Symposium (GD '03). volume 2912 of Lecture Notes in Computer Science, pages 345-356. Springer-Verlag, Berlin, 2003.
21. K. Sugiyama, S. Tagawa, and M. Toda, Methods for visual understanding of hierarchical system structures. IEEE Trans. Systems Man Cybernet., 11(2):109-125, 1981.
22. N. Tomii, Y. Kambayashi, and S. Yajima. On planarization algorithms of 2-level graphs. IECEJ, EC77-38:1-12, 1977.
23. V. Valls, R. Marti, and P. Lino. A branch and bound algorithm for minimizing the number of crossing arcs in bipartite graphs. J. Oper Res., 90:303-319, 1996.
24. J. N. Warfield. Crossing theory and hierarchy mapping. IEEE Trans. Systems Man Cybernet., 7(7):505-523, 1977.
25. M. S. Waterman and J. R. Griggs. Interval graphs and maps of DNA. Bull. Math. Biol., 48(2): 189-195, 1986.