Maximizing the Total Resolution of Graphs

TL;DR

This paper introduces the concept of total resolution in graph drawings, combining angular and crossing resolutions, and presents optimal constructions and a force-directed algorithm to maximize it.

Contribution

It is the first to study maximizing total resolution, providing asymptotically optimal drawings for complete and bipartite graphs, and a new force-directed algorithm.

Findings

Optimal total resolution drawings for complete graphs

Optimal total resolution drawings for bipartite graphs

Force-directed algorithm effectively increases total resolution

Abstract

A major factor affecting the readability of a graph drawing is its resolution. In the graph drawing literature, the resolution of a drawing is either measured based on the angles formed by consecutive edges incident to a common node (angular resolution) or by the angles formed at edge crossings (crossing resolution). In this paper, we evaluate both by introducing the notion of "total resolution", that is, the minimum of the angular and crossing resolution. To the best of our knowledge, this is the first time where the problem of maximizing the total resolution of a drawing is studied. The main contribution of the paper consists of drawings of asymptotically optimal total resolution for complete graphs (circular drawings) and for complete bipartite graphs (2-layered drawings). In addition, we present and experimentally evaluate a force-directed based algorithm that constructs drawings of large total resolution.