Optimal Angular Resolution for Face-Symmetric Drawings

TL;DR

This paper presents a polynomial-time method for creating face-symmetric graph drawings that maximize the smallest angle between incident edges, improving visual clarity in graph visualization.

Contribution

It introduces a polynomial-time algorithm for optimizing angular resolution in face-symmetric drawings by reducing the problem to parametric shortest paths.

Findings

The algorithm runs in at most O(t^3) time, with t typically proportional to the square root of the number of vertices.

It guarantees maximized minimum incident edge angles in face-symmetric drawings.

The approach enhances the aesthetic and readability quality of graph visualizations.

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.