An efficient implementation of Sugiyama's algorithm for layered graph drawing

Sugiyama's algorithmic framework for layered graph drawing is commonly used in practical software. The extensive use of dummy vertices to break long edges between non-adjacent layers often leads to unsatisfactorial performance. The worst-case running-time of Sugiyama's approach is O(vertical bar V vertical bar vertical bar E vertical bar log vertical bar E vertical bar) requiring O(vertical bar V vertical bar vertical bar E vertical bar) memory, which makes it unusable for the visualization of large graphs. By a conceptually simple new technique we are able to keep the number of dummy vertices and edges linear in the size of the graph and hence reduce the worst-case time complexity of Sugiyama's approach by an order of magnitude to O((vertical bar V vertical bar + vertical bar E vertical bar) log vertical bar E vertical bar) requiring O(vertical bar V vertical bar + vertical bar E vertical bar) space.