Abstract
We investigate the problem of constructing planar straightline drawings of graphs with large angles between the edges. Namely, we study the angular resolution of planar straight-line drawings, defined as the smallest angle formed by two incident edges. We prove the first nontrivial upper bound on the angular resolution of planar straight-line drawings, and show a continuous trade-off between the area and the angular resolution. We also give linear-time algorithms for constructing planar straight-line drawings with high angular resolution for various classes of graphs, such as series-parallel graphs, outerplanar graphs, and triangulations generated by nested triangles. Our results are obtained by new techniques that make extensive use of geometric constructions.
Research supported in part by the National Science Foundation under grant CCR-9007851, by the U.S. Army Research Office under grants DAAL03-91-G-0035 and DAAH04-93-0134, and by the Office of Naval Research and the Defense Advanced Research Projects Agency under contract N00014-91-J-4052, ARPA order 8225.
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© 1994 Springer-Verlag Berlin Heidelberg
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Garg, A., Tamassia, R. (1994). Planar drawings and angular resolution: Algorithms and bounds. In: van Leeuwen, J. (eds) Algorithms — ESA '94. ESA 1994. Lecture Notes in Computer Science, vol 855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049393
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DOI: https://doi.org/10.1007/BFb0049393
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