Some step-by-step thoughts & possibilities:
- step-by-step might be too fine-grained for many graphs
- both mincross (phase 2) & ns (phase 3) can be terminated early
- using mclimit (mclimit | Graphviz) for mincross
- using nslimit (nslimit | Graphviz) for ns
- the code for the above might have to be modified for the desired granularity
- then use the appropriate value for phase to produce a dot-format output, as for illustrateDot (above)
- phase 2 would seem to present a set of images showing nodes hopping left & right on their appointed ranks
- phase 3 would show the nodes sliding left & right, but keeping their appointed order.
- the spline boxes only apply to phase 4 and can be applied via post-processing (similar to Fun with edges!)