Optimal Angular Resolution for Face-Symmetric Drawings
@article{Eppstein2009OptimalAR, title={Optimal Angular Resolution for Face-Symmetric Drawings}, author={David Eppstein and Kevin A. Wortman}, journal={J. Graph Algorithms Appl.}, year={2009}, volume={15}, pages={551-564} }
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…
4 Citations
Angle Optimization of Graphs Embedded in the Plane
- Computer Science, MathematicsArXiv
- 2012
This paper considers the problem of maximizing the minimum angle, the MMA problem, using a spring-embedding approach where two forces are applied to the vertices of the graph: a force optimizing edge lengths and a force optimize angles.
Graph-Theoretic Solutions to Computational Geometry Problems
- Computer ScienceWG
- 2009
The art gallery problem, partition into rectangles, minimum-diameter clustering, rectilinear cartogram construction, mesh stripification, angle optimization in tilings, and metric embedding are surveyed from a graph-theoretic perspective.
Combinatorics and Geometry of Finite and Infinite Squaregraphs
- MathematicsSIAM J. Discret. Math.
- 2010
It is shown that minimum-size median-generating sets of finite squaregraphs can be computed in polynomial time, whereas, not unexpectedly, the corresponding problem for median graphs turns out to be NP-hard.
Edge Bounds and Degeneracy of Triangle-Free Penny Graphs and Squaregraphs
- MathematicsJ. Graph Algorithms Appl.
- 2018
We show that triangle-free penny graphs have degeneracy at most two, and that both triangle-free penny graphs and squaregraphs have at most min ( 2n − Ω( √ n), 2n −D − 2 ) edges, where n is the…
References
SHOWING 1-10 OF 11 REFERENCES
Trees with Convex Faces and Optimal Angles
- Mathematics, Computer ScienceGraph Drawing
- 2006
This work considers drawings of trees in which all edges incident to leaves can be extended to infinite rays without crossing, partitioning the plane into infinite convex polygons, and finds linear time algorithms for solving this problem.
On the angular resolution of planar graphs
- MathematicsSTOC '92
- 1992
A very natural linear program is analyzed that bounds the angular resolution of any fixed planar graph G from &OHgr;(1/<italic>d</italic>, although currently, it is unable to settle whether or not this lower bound is existentially tight (up to constant α).
Combinatorics and Geometry of Finite and Infinite Squaregraphs
- MathematicsSIAM J. Discret. Math.
- 2010
It is shown that minimum-size median-generating sets of finite squaregraphs can be computed in polynomial time, whereas, not unexpectedly, the corresponding problem for median graphs turns out to be NP-hard.
Parametric shortest path algorithms with an application to cyclic staffing
- Computer Science, MathematicsDiscret. Appl. Math.
- 1981
Algorithms for Drawing Media
- Computer ScienceGD
- 2004
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…
Parametric Combinatorial Computing and a Problem of Program Module Distribution
- Mathematics, Computer ScienceJACM
- 1983
On propose une methode de calcul parametrique generale, efficace pour une large classe of problemes combinatoires par Megiddo pour the resolution de problemes d'optimisation de ratios.
Center and diameter problem in planar quadrangulations and triangulations
- Proc. 13th ACM-SIAM Symp. Discrete Algorithms (SODA), pages 346–355
- 2002
Parametric cost shortest path problems
- Unpublished Bellcore memo
- 1984