notes for gim on graph drawing algo, and some TODOs

gg/gg.go

@@ -8,6 +8,22 @@ import (
 	"strings"
 )
 
+// TODO it's a bit unfortunate that it's possible to create disjointed graphs
+// within the same graph instance. That's not really something that would be
+// possible with any other type of datastructure. I think all that would be
+// needed to get rid of this is to remove the Null instance and instead do a
+// New(value) function. This would allow a graph to be just a single value with
+// no edges, but I _think_ that's fine?
+//
+// Actually, that's kinda bogus, it really messes with how I conceptualized
+// ginger being used. Which is maybe fine. I should do some research on the
+// typical way that graphs and other structures are defined.
+//
+// It seems that disjoint unions, as they're called, are an accepted thing... if
+// I need it for gim a Disjoin method might be the best bet, which would walk
+// through the Graph and compute each disjointed Graph and return them
+// individually.
+
 // Value wraps a go value in a way such that it will be uniquely identified
 // within any Graph and between Graphs. Use NewValue to create a Value instance.
 // You can create an instance manually as long as ID is globally unique.

gim/NOTES

@@ -0,0 +1,71 @@
+Notes from reading https://www.graphviz.org/Documentation/TSE93.pdf, which
+describes an algorithm for drawing an acyclic graph in basically the way which I
+want.
+
+This document assumes the primary flow of drawing is downward, and secondary is
+right.
+
+For all of this it might be easier to not even consider edge values yet, as
+those could be done by converting them into vertices themselves after the
+cyclic-edge-reversal and then converting them back later.
+
+Drawing the graph is a four step process:
+
+1) Rank nodes in the Y axis
+    - Graph must be acyclic.
+        - This can be accomplished by strategically reversing edges which cause
+          a cycle, and then reversing them back as a post-processing step.
+        - Edges can be found by:
+            - walking out from a particular node depth-first from some arbitrary
+              node.
+            - As you do so you assign a rank based on depth to each node you
+              encounter.
+            - If any edge is destined for a node which has already been seen you
+              look at the ranks of the source and destination, and if the source
+              is _greater_ than the destination you reverse the edge's
+              direction.
+        - I think that algorithm only works if there's a source/sink? might have
+          to be modified, or the walk must traverse both to & from.
+    - Assign all edges a weight, default 1, but possibly externally assigned to
+      be greater.
+    - Take a "feasible" minimum spanning tree (MST) of the graph
+        - Feasibility is defined as each edge being "tight", meaning, once you
+          rank each node by their distance from the root and define the length
+          of an edge as the difference of rank of its head and tail, that each
+          tree edge will have a length of 1.
+    - Perform the following on the MST:
+        - For each edge of the graph assign the cut value
+            - If you were to remove any edge of an MST it would create two
+              separate MSTs. The side the edge was pointing from is the tail,
+              the side it was pointing to is the head.
+            - Looking at edges _in the original graph_, sum the weights of all
+              edges directed from the tail to the head (including the one
+              removed) and subtract from that the sum of the weights of the
+              edges directed from the head to the tail. This is the cut value.
+            - "...note that the cut values can be computed using information
+              local to an edge if the search is ordered from the leaves of the
+              feasible tree inward. It is trivial to compute the cut value of a
+              tree edge with one of its endpoints a leaf in the tree, since
+              either the head or the tail component consists of a single node.
+              Now, assuming the cut values are known for all the edges incident
+              on a given node except one, the cut value of the remaining edge is
+              the sum of the known cut values plus a term dependent only on the
+              edges incident to the given node."
+        - Take an edge with a negative cut value and remove it. Find the graph
+          edge between the remaining head and tail MSTs with the smallest
+          "slack" (distance in rank between its ends) and add that edge to the
+          MST to make it connected again.
+        - Repeat until there are no negative cut values.
+        - Apparently searching "cyclically" through the negative edges, rather
+          than iterating from the start each time, is worthwhile.
+    - Normalize the MST by assigning the root node the rank of 0 (and so on), if
+      it changed.
+    - All edges in the MST are of length 1, and the rest can be inferred from
+      that.
+    - To reduce crowding, nodes with equal in/out edge weights and which could
+      be placed on multiple rankings are moved to the ranking with the fewest
+      nodes.
+
+2) Order nodes in the X axis to reduce edge crossings
+3) Compute node coordinates
+4) Determine edge splines

gim/main.go

@@ -16,10 +16,8 @@ import (
 // - Changing the "flow" direction
 // - Absolute positioning of some/all vertices
 
-// TODO
+// TODO be able to draw circular graphs
-// - edge values
+// TODO audit all steps, make sure everything is deterministic
-// - be able to draw circular graphs
-// - audit all steps, make sure everything is deterministic
 
 const (
 	framerate   = 10