Hierarchical Graph Drawing

The drawing of hierarchical graphs is one of the main areas of research in the field of Graph Drawing. In this paper we study the problem of partitioning the node set of a directed acyclic graph into layers — the first step of the commonly accepted Sugiyama algorithm for drawing directed acyclic graphs as hierarchies. We present a combinatorial optimization approach to the layering problem; we define a graph layering polytope and describe its properties in terms of facet-defining inequalities. The theoretical study presented is the basis of a new branch-and-cut layering algorithm which produces better quality drawings of hierarchical graphs.

We propose two fast heuristics for solving the NP-hard problem of graph layering with the minimum width and consideration of dummy nodes. Our heuristics can be used at the layer-assignment phase of the Sugiyama method for drawing of directed graphs. We evaluate our heuristics by comparing them to the widely used fast-layering algorithms in an extensive computational study with nearly 6000 input graphs. We also demonstrate how the well-known longest-path and Coffman--Graham algorithms can be used for finding narrow layerings with acceptable aesthetic properties.

This paper presents the design and implementation of an ant colony optimization based algorithm for solving the DAG layering problem. This algorithm produces compact layerings by minimising their width and height. Importantly it takes into account the contribution of dummy vertices to the width of the resulting layering.