A Generalization of the Directed Graph Layering Problem

TL;DR

This paper introduces the Generalized Layering Problem (GLP), which combines graph acyclicity and layering into a single approach, enabling more efficient and compact graph drawings for general graphs.

Contribution

It presents an integer programming model and heuristic for the NP-complete GLP, integrating feedback arc set and layering problems into one framework.

Findings

GLP reduces dummy nodes significantly

GLP produces more compact graph drawings

GLP improves aspect ratios on complex graphs

Abstract

The Directed Layering Problem (DLP) solves a step of the widely used layer-based approach to automatically draw directed acyclic graphs. To cater for cyclic graphs, usually a preprocessing step is used that solves the Feedback Arc Set Problem (FASP) to make the graph acyclic before a layering is determined. Here we present the Generalized Layering Problem (GLP), which solves the combination of DLP and FASP simultaneously, allowing general graphs as input. We present an integer programming model and a heuristic to solve the NP-complete GLP and perform thorough evaluations on different sets of graphs and with different implementations for the steps of the layer-based approach. We observe that GLP reduces the number of dummy nodes significantly, can produce more compact drawings, and improves on graphs where DLP yields poor aspect ratios.