Abstract
We describe algorithms for drawing media, systems of states, tokens and actions that have state transition graphs in the form of partial cubes. Our algorithms are based on two principles: embedding the state transition graph in a low-dimensional integer lattice and projecting the lattice onto the plane, or drawing the medium as a planar graph with centrally symmetric faces.
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Aurenhammer, F., Hagauer, J.: Recognizing binary Hamming graphs in O(n 2 log n) time. Mathematical Systems Theory 28, 387–395 (1995)
Bhatt, S., Cosmodakis, S.: The complexity of minimizing wire lengths in VLSI layouts. Inform. Proc. Lett. 25, 263–267 (1987)
Chan, T.M.: On levels in arrangements of curves. Discrete & Comput. Geom. 29(3), 375–393 (2003)
Di Battista, G., Tamassia, R.: Incremental planarity testing. In: Proc. 30th IEEE Symp. Foundations of Computer Science (FOCS 1989), pp. 436–441 (1989)
Eppstein, D.: Layered graph drawing, http://www.ics.uci.edu/~eppstein/junkyard/thickness/
Eppstein, D.: The lattice dimension of a graph. To appear in Eur. J. Combinatorics, arXiv:cs.DS/0402028 (to appear)
Eppstein, D., Falmagne, J.-C.: Algorithms for media. ACM Computing Research Repository (June 2002) arXiv:cs.DS/0206033
Falmagne, J.-C., Ovchinnikov, S.: Media theory. Discrete Applied Mathematics 121(1–3), 103–118 (2002)
de Fraysseix, H., Ossona de Mendez, P.: Stretching of Jordan arc contact systems. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 71–85. Springer, Heidelberg (2004)
Goodman, J.E., Pollack, R.: Allowable sequences and order types in discrete and computational geometry. In: New Trends in Discrete and Computational Geometry. Algorithms and Combinatorics 10, ch. V, pp. 103–134. Springer, Heidelberg (1993)
Imrich, W., Klavžar, S.: On the complexity of recognizing Hamming graphs and related classes of graphs. Eur. J. Combinatorics 17, 209–221 (1996)
Imrich, W., Klavžar, S.: Product Graphs. John Wiley & Sons, Chichester (2000)
Mutzel, P.: The SPQR-tree data structure in graph drawing. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 34–46. Springer, Heidelberg (2003)
Ovchinnikov, S.: The lattice dimension of a tree. arXiv.org (February 2004) arXiv:math.CO/0402246
Winkler, P.: Isometric embeddings in products of complete graphs. Discrete Applied Mathematics 7, 221–225 (1984)
Wong, T.-T., Luk, W.-S., Heng, P.-A.: Sampling with Hammersley and Halton points. J. Graphics Tools 2(2), 9–24 (1997)
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Eppstein, D. (2005). Algorithms for Drawing Media. In: Pach, J. (eds) Graph Drawing. GD 2004. Lecture Notes in Computer Science, vol 3383. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31843-9_19
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DOI: https://doi.org/10.1007/978-3-540-31843-9_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24528-5
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