[DO NOT MERGE] try Kahn's toposort

[dmaskasky]

FOR DEMONSTRATION PURPOSES ONLY

Related: #2821 (comment)

Summary

Kahn's Topological Sort uses an iterative BFS approach to sort nodes in a DAG. It uses in-degrees a count of the number of remaining unsorted dependencies a node as. As nodes are sorted, in-degrees is decremented. When in-degrees reaches zero for a node, that node is appended to the sorted set.

The difficulty with using Kahn's in our application is that we first need to do a bunch of expensive admin work.

• construct a map of all dependent nodes to their dependents. Implemented here is an iterative BFS solution, but a DFS approach has the same complexity
• create a map of every atom to their in-degree
• iterate through all atoms and enqueu where in-degree === 0

The result averages (100x) show that Kahns runs ~25% slower than iterative DFS.

--------------------------------------------------------------------------------
LINEAR
kahnsToposort: 25.4166
getSortedDependents: 20.7627
kahn times are 22.4148 percent slower than iterative DFS
--------------------------------------------------------------------------------
STAR
kahnsToposort: 22.9688
getSortedDependents: 19.8854
kahn times are 15.5060 percent slower than iterative DFS
--------------------------------------------------------------------------------
K-ARY
kahnsToposort: 26.1628
getSortedDependents: 21.1882
kahn times are 23.4780 percent slower than iterative DFS

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See documentations for usage instructions.

[dmaskasky]

Update: if I use indexes instead of map, its a little faster but more ugly.

LINEAR --------------------------------------------------------------------------------
kahnsToposort: 18.4981
getSortedDependents: 18.0733
kahn times are 2.3504 percent slower than toposort
STAR --------------------------------------------------------------------------------
kahnsToposort: 19.8348
getSortedDependents: 20.3942
kahn times are 2.7431 percent faster than toposort
K-ARY --------------------------------------------------------------------------------
kahnsToposort: 20.2995
getSortedDependents: 20.3445
kahn times are 0.2209 percent faster than toposort

[dmaskasky]

Update: using arrays seems to help

LINEAR --------------------------------------------------------------------------------
kahnsToposort: 20.1562
getSortedDependents: 20.0564
kahn times are 0.4973 percent slower than toposort
STAR --------------------------------------------------------------------------------
kahnsToposort: 17.1281
getSortedDependents: 20.2366
kahn times are 15.3605 percent faster than toposort
K-ARY --------------------------------------------------------------------------------
kahnsToposort: 19.4536
getSortedDependents: 19.6978
kahn times are 1.2398 percent faster than toposort

[dmaskasky]

Closing this for now. While Kahn's algorithm is slightly faster for extremely large K-Ary and Star graphs, it comes with higher memory overhead and performs worse on smaller atom graphs. Given that the average case involves smaller atom graphs, I don't believe the added complexity of Kahn's algorithm is justified.