Abstract
In this paper we investigate the problem of constructing planar straight-line drawings of acyclic digraphs such that all the edges flow in the same direction, e.g., from bottom to top. Our contribution is twofold. First we show the existence of a family of planar acyclic digraphs that require exponential area for any such drawing. Second, motivated by the preceding lower bound, we relax the straight-line constraint and allow bends along the edges. We present a linear-time algorithm that produces drawings of planarst-graphs with a small number of bends, asymptotically optimal area, and such that symmetries and isomorphisms of the digraph are displayed. If the digraph has no transitive edges, then the drawing obtained has no bends. Also, a variation of the algorithm produces drawings with exact minimum area.
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Research supported in part by Cadre Technologies Inc., by the ESPRIT II Basic Research Actions Program of the EC under Contract No. 3075 (project ALCOM), by the National Science Foundation under Grant CCR-9007851, by the Office of Naval Research and the Defense Advanced Research Projects Agency under Contract N00014-83-K-0146 and ARPA order 6320, amendment 1, by the Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo of the Italian National Research Council, by the Texas Advanced Research Program under Grant No. 3972, and by the U.S. Army Research Office under Grant DAAL03-91-G-0035.
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Battista, G.D., Tamassia, R. & Tollis, I.G. Area requirement and symmetry display of planar upward drawings. Discrete Comput Geom 7, 381–401 (1992). https://doi.org/10.1007/BF02187850
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DOI: https://doi.org/10.1007/BF02187850