Optimal Angular Resolution for FaceSymmetric Drawings
Abstract
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 typically proportional to n^.5.
 Publication:

arXiv eprints
 Pub Date:
 July 2009
 arXiv:
 arXiv:0907.5474
 Bibcode:
 2009arXiv0907.5474E
 Keywords:

 Computer Science  Data Structures and Algorithms;
 G.2.2
 EPrint:
 10 pages, 6 figures