Grid sifting

Abstract

Directed graphs are commonly drawn by the Sugiyama algorithm where first vertices are placed on distinct hierarchical levels, and second vertices on the same level are permuted to reduce the overall number of crossings. Separating these two phases simplifies the algorithms but diminishes the quality of the result. We introduce a combined leveling and crossing reduction algorithm based on sifting, which prioritizes few crossings over few levels. It avoids type 2 conflicts, which are crossings of edges whose endpoints are dummy vertices. This helps straightening long edges spanning many levels. The obtained running time is roughly quadratic in the size of the input graph and independent of dummy vertices.