Add Optimal Sugiyama Layout

[oxinabox]

I am actually working more off this paper
https://ialab.it.monash.edu/~dwyer/papers/optimal-sankey-diagrams.pdf

so perhaps it should be a ZarateLayout ?

TODO

• Dummy Nodes
• Permuting Order
• Arranging
• Weights for crossings
• Do the perfomance constraint tweaks mentioned in the paper
• Option to try multiple equally good orderings to see if any yeild better arrangement score.
• Rewrite Arrangement subproblem from a QP into a SOCP and swap to ECOS
• Vertically center the graph (right now the vertical position is basically arbitary, and thigns tend to be anywherre from 25-100, but really could be up in 10_000s or anywhere). Potentially this might cause stability issues (which centering in post would not fix)

Also supports weights for crossings so should be perfect for Sankey
(cc @daschw)

[daschw]

Oooh, that looks amazing. Thanks for pinging!

[oxinabox]

@daschw for a Sankey diagram should the weights control the distance during arrangement, or just how hard to try for different overlapping line-crossings during ordering?

Currently it does both.
Which is why the 5 and 5 are lifted up in the diagram shown above.
The Tension from the 3->5 line is greater than that from the 3->6 line, so it pulls it up.

[oxinabox]

Oh wow my git settings are a total mess

[oxinabox]

I added checking for multiple solutions. It doesn't find many that are better than but does find some that are better in the like 10^-7 order or something.
and lots that are worse (in the 10^0 order), which suggests either something special about the first, or just getting lucky.

[daschw]

@daschw for a Sankey diagram should the weights control the distance during arrangement, or just how hard to try for different overlapping line-crossings during ordering?

Sorry, I missed this question. Looking at e.g. https://observablehq.com/@d3/sankey-diagram it does not seem like the weights impact the distance. It rather looks the maximum yaxis range is minimized.

[oxinabox]

Looking at e.g. https://observablehq.com/@d3/sankey-diagram it does not seem like the weights impact the distance. It rather looks the maximum yaxis range is minimized.

Cool, if we remove the weighting from that step then that is what we will have.
our notion of score for the distance step is the (currently weighted) sum of y-axis differences between connected vertexs. Which i think is what you are saying?

[oxinabox]

I think this basically done.
Its no where near as fast as the paper claims, but that could be the difference in solvers.
Probably will merge it soon.
Need to workout what is up with the CI first

[oxinabox]

with enhancements that are in the commit i am about to push was able to solve the large dep graph in 67 seconds

[oxinabox]

For some reason coveralls is failing to upload but tests are passing

[daschw]

I finally managed to continue work on this : https://github.com/daschw/SankeyPlots.jl