Multi-level Verticality Optimization: Concept, Strategies, and Drawing Scheme

In traditional multi-level graph drawing|known as Sugi- yama's framework|the number of crossings is considered one of the most important goals. Herein, we propose the alternative concept of optimiz- ing the verticality of the drawn edges. We formally specify the problem, discuss its relative merits, and show that drawings that are good w.r.t. verticality in fact also have a low number of crossings. We present heuris- tic and exact approaches to tackle the verticality problem and study them in practice. Furthermore, we present a new drawing scheme (inherently bundling edges and drawing them monotonously), especially suitable for verticality optimization. It works without the traditional subdivision of edges, i.e., edges may span multiple levels, and therefore potentially allows to tackle larger graphs.