Abstract
We consider the problem of drawing a directed graph in two dimensions with a minimum number of crossings such that for every node the incoming edges appear consecutively in the cyclic adjacency lists. We show how to adapt the planarization method and the recently devised exact crossing minimization approach in a simple way. We report experimental results on the increase in the number of crossings involved by this additional restriction on the set of feasible drawings. It turns out that this increase is negligible for most practical instances.
Partially supported by the Marie Curie RTN ADONET 504438 funded by the EU.
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Bertolazzi, P., Di Battista, G., Didimo, W.: Quasi-upward planarity. Algorithmica 32, 474–506 (2002)
Buchheim, C., Ebner, D., Jünger, M., Klau, G.W., Mutzel, P., Weiskircher, R.: Exact Crossing Minimization. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 37–48. Springer, Heidelberg (2006)
Djidjev, H.N.: A linear algorithm for the maximal planar subgraph problem. In: Sack, J.-R., Akl, S.G., Dehne, F., Santoro, N. (eds.) WADS 1995. LNCS, vol. 955, pp. 369–380. Springer, Heidelberg (1995)
Faria, L., de Figueiredo, C.M.H., de Mendonça, N.C.F.X.: Splitting number is NP-complete. Discrete Applied Mathematics 108(1–2), 65–83 (2001)
Garey, M.R., Johnson, D.S.: Crossing number is NP-complete. SIAM Journal on Algebraic and Discrete Methods 4(3), 312–316 (1983)
Gutwenger, C., Mutzel, P., Weiskircher, R.: Inserting an edge into a planar graph. Algorithmica 41(4), 289–308 (2005)
Hliněný, P.: Crossing number is hard for cubic graphs. In: MCFS 2004, pp. 772–782 (2003)
Jayakumar, R., Thulasiraman, K., Swamy, M.N.S.: O(n 2) algorithms for graph planarization. IEEE Transactions on Computer-Aided Design 8, 257–267 (1989)
Jünger, M., Mutzel, P.: Maximum planar subgraphs and nice embeddings: Practical layout tools. Algorithmica 16(1), 33–59 (1996)
La Poutré, J.A.: Alpha-algorithms for incremental planarity testing. In: STOC 1994, pp. 706–715 (1994)
Liebers, A.: Planarizing graphs – a survey and annotated bibliography. Journal of Graph Algorithms and Applications 5(1), 1–74 (2001)
Menze, A.: Darstellung von Nebenmetaboliten in automatisch erzeugten Zeichnungen metabolischer Netzwerke. Master’s thesis, Institute of Biochemistry, University of Cologne (June 2004)
Pelsmajer, M.J., Schaefer, M., Štefankovič, D.: Crossing number of graphs with rotation systems. Technical report, Department of Computer Science, DePaul University (2005)
Rome library of directed graphs, http://www.inf.uniroma3.it/people/gdb/wp12/directed-acyclic-1.tar.gz
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Buchheim, C., Jünger, M., Menze, A., Percan, M. (2006). Bimodal Crossing Minimization. In: Chen, D.Z., Lee, D.T. (eds) Computing and Combinatorics. COCOON 2006. Lecture Notes in Computer Science, vol 4112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11809678_52
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DOI: https://doi.org/10.1007/11809678_52
Publisher Name: Springer, Berlin, Heidelberg
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