L-Drawings of Directed Graphs

TL;DR

This paper introduces L-drawings, a new way to visualize directed graphs combining orthogonal readability with matrix-like expressiveness, and studies the computational complexity and heuristics for their minimal ink representations.

Contribution

It presents the concept of L-drawings, proves the NP-completeness of the minimum ink problem, and develops a polynomial-time heuristic with experimental validation.

Findings

NP-completeness of minimum ink L-drawings

Effective heuristic for adding vertices with minimal ink

Experimental results confirm heuristic's effectiveness

Abstract

We introduce L-drawings, a novel paradigm for representing directed graphs aiming at combining the readability features of orthogonal drawings with the expressive power of matrix representations. In an L-drawing, vertices have exclusive $x$- and $y$-coordinates and edges consist of two segments, one exiting the source vertically and one entering the destination horizontally. We study the problem of computing L-drawings using minimum ink. We prove its NP-completeness and provide a heuristics based on a polynomial-time algorithm that adds a vertex to a drawing using the minimum additional ink. We performed an experimental analysis of the heuristics which confirms its effectiveness.