GraphViz: trouble with grid layout using pos attribute - graphviz

Question

I'm trying to align this graph, whose purpose is to show the results of sorting.
I need a general solution.
The dot file is generated, so I can't use hand tweaking.
I've tried pos, pos with !, dot -n, dot -Kneato, dot -Kfdp, and other things.
Here is the source (laid out for human grokkability):
digraph x {
rankdir=LR
11 [pos="1,1"] 21 [pos="2,1"] 31 [pos="3,1"] 41 [pos="4,1"]
12 [pos="1,2"] 22 [pos="2,2"] 32 [pos="3,2"] 42 [pos="4,2"]
13 [pos="1,3"] 23 [pos="2,3"] 33 [pos="3,3"]
14 [pos="1,4"] 24 [pos="2,4"]
11:e -> 21:w 21:e -> 31:w 31:e -> 41:w
12:e -> 22:w 22:e -> 32:w 32:e -> 42:w
22:e -> 31:w
# 41:e -> 21:w
# 41:e -> 22:w
# 12:e -> 12:w
# 32:e -> 32:w
13:e -> 23:w 23:e -> 33:w
14:e -> 24:w
# 13:e -> 14:w
# 14:e -> 13:w
# 23:e -> 24:w
# 24:e -> 23:w
}
In the first rendering, you'll see essentially how it should look (except for the shuffled row order).
Later renderings, which will include cyclic edges, should retain this basic layout.
dot -Tpng -o test.png test.dot:
Now some renderings after uncommenting the cyclic edges.
dot -Tpng -o test.png test.dot:
dot -Kneato -Tpng -o test.png test.dot:
dot -Kfdp -Tpng -o test.png test.dot:

Answer 1

Not using pos as in my experience (confirmed by your attempts), it does not work well with the dot engine, and with neato and others I have never been able to produce something like a grid layout.
Three general steps to get closer with dot:
align the nodes vertically with rank = same
align the nodes horizontally using weight = 10 (or any other arbitrary number that works)
add invisible vertical struts as necessary (here 14 -> 12)
make sure that you point the edges following the established hierarchy, meaning explicitly using dir = back where appropriate
My shot at your situation:
digraph
{
rankdir = LR;
{rank = same; 14 -> 13 -> 12 -> 11[ style = invis ] }
{rank = same; 24 -> 23 -> 22 -> 21[ style = invis ] }
{rank = same; 33 -> 32 -> 31[ style = invis ] }
{rank = same; 42 -> 41[ style = invis ] }
14 -> 24[ weight = 10 ];
13 -> 23 -> 33[ weight = 10 ];
12 -> 22 -> 32 -> 42[ weight = 10 ];
11 -> 21 -> 31 -> 41[ weight = 10 ];
22:e -> 31:w;
12:e -> 12:w
32:e -> 32:w
21:se -> 41:sw[ dir = back ];
22:se -> 41:sw[ dir = back ];
14 -> 12 [ color = red ];
14:w -> 13:w
13:e -> 14:e[ dir = back ];
24:w -> 23:w
23:e -> 24:e[ dir = back ];
}
which yields