Optimal Angular Resolution for Face-Symmetric Drawings

@article{Eppstein2011OptimalAR,
  title={Optimal Angular Resolution for Face-Symmetric Drawings},
  author={David Eppstein and Kevin A. Wortman},
  journal={ArXiv},
  year={2011},
  volume={abs/0907.5474}
}
  • David Eppstein, Kevin A. Wortman
  • Published 2011
  • Computer Science, Mathematics
  • ArXiv
  • Let G be a graph that may be drawn in the plane in such a way that all internal faces are centrally symmetric convex polygons. We show how to find a drawing of this type that maximizes the angular resolution of the drawing, the minimum angle between any two incident edges, in polynomial time, by reducing the problem to one of finding parametric shortest paths in an auxiliary graph. The running time is at most O(t^3), where t is a parameter of the input graph that is at most O(n) but is more… CONTINUE READING

    Citations

    Publications citing this paper.
    SHOWING 1-2 OF 2 CITATIONS

    Angle Optimization of Graphs Embedded in the Plane

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    CITES BACKGROUND

    Graph-Theoretic Solutions to Computational Geometry Problems

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    CITES METHODS

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 12 REFERENCES

    Trees with Convex Faces and Optimal Angles

    VIEW 3 EXCERPTS

    On the angular resolution of planar graphs

    VIEW 1 EXCERPT

    Combinatorics and Geometry of Finite and Infinite Squaregraphs

    VIEW 1 EXCERPT

    Parametric shortest path algorithms with an application to cyclic staffing

    VIEW 7 EXCERPTS
    HIGHLY INFLUENTIAL

    A triangle-free circle graph with chromatic number 5

    VIEW 2 EXCERPTS

    Algorithms for Drawing Media

    VIEW 10 EXCERPTS

    Media theory

    VIEW 1 EXCERPT

    Center and diameter problem in planar quadrangulations and triangulations

    • V. Chepoi, F. Dragan, Y. Vaxès
    • Proc. 13th ACM-SIAM Symp. Discrete Algorithms (SODA), pages 346–355
    • 2002
    VIEW 1 EXCERPT

    Output of our implementation for the graph shown in Figure 1, safely optimized (left) and unsafely optimized (right)

    • Figure