Crthuky

I'm trying to use layered graph layouts to generate Directed Acyclic Graphs where all nodes are partitioned into layers. The following code produces a near-perfect result.

RequirePackageluatex85
documentclassarticle

usepackagegraphicx
usepackagesubcaption
usepackagea4wide

usepackagetikz
usetikzlibrarygraphs,graphdrawing,quotes
usegdlibrarylayered

begindocument
beginfigure
centering
beginsubfigure[]0.3textwidth
centering
begintikzpicture[rounded corners]
graph [layered layout,
edge quotes=fill=white,inner sep=1pt,font=scriptsize,
nodes=circle,draw,inner sep=.2,outer sep=0, minimum size=.45cm,
level sep=1.5cm, %vertical distance between layers
sibling distance=2cm, %distance between nodes of the same connected component in the same layer
component sep=0cm %distance between connected components
]


[nodes=draw=none,text opacity=0, edge=draw=none]
l0 ->["$v0$"] l1 ->["$v1$"] l2 ->["$v2$"] l3 ->["$v4$"] l4 ->["$v5$"] l5;
,
[edge=pos=.45]
r/"$r$";
t/"$t$";
2/"$u_2$";
3/"$u_3$";
4/"$u_4$";
5/"$u_5$";
6/"$u_6$";
7/"$u_7$";
8/"$u_8$";
9/"$u_9$";
10/"$u_10$";
11/"$u_11$";
12/"$u_12$";
r ->["$0$",bend left=0] 2,
r ->["$1$",bend left=0] 3,
2 ->["$0$",bend left=0] 4,
2 ->["$1$",bend left=0] 5,
3 ->["$0$",bend left=0] 6,
3 ->["$1$",bend left=0] 4,
4 ->["$0$",bend left=0] 7,
4 ->["$1$",bend left=0] 8,
5 ->["$0$",bend left=0] 9,
5 ->["$1$",bend left=0] 7,
6 ->["$0$",bend left=0] 8,
6 ->["$1$",bend left=0] 9,
7 ->["$0$",bend left=0] 10,
7 ->["$1$",bend left=0] 11,
8 ->["$0$",bend left=0] 12,
8 ->["$1$",bend left=0] 10,
9 ->["$0$",bend left=0] 11,
9 ->["$1$",bend left=0] 12,
10 ->["$1$",bend left=-80] t,
10 ->["$4$",bend left=-60] t,
10 ->["$7$",bend left=-40] t,
10 ->["$10$",bend left=-20] t,
10 ->["$13$",bend left=0] t,
10 ->["$16$",bend left=20] t,
10 ->["$19$",bend left=40] t,
10 ->["$22$",bend left=60] t,
10 ->["$25$",bend left=80] t,
11 ->["$0$",bend left=-80] t,
11 ->["$3$",bend left=-60] t,
11 ->["$6$",bend left=-40] t,
11 ->["$9$",bend left=-20] t,
11 ->["$12$",bend left=0] t,
11 ->["$15$",bend left=20] t,
11 ->["$18$",bend left=40] t,
11 ->["$21$",bend left=60] t,
11 ->["$24$",bend left=80] t,
12 ->["$2$",bend left=-80] t,
12 ->["$5$",bend left=-60] t,
12 ->["$8$",bend left=-40] t,
12 ->["$11$",bend left=-20] t,
12 ->["$14$",bend left=0] t,
12 ->["$17$",bend left=20] t,
12 ->["$20$",bend left=40] t,
12 ->["$23$",bend left=60] t,

;
beginscope[node distance=.4cm,font=scriptsize]
node[right of=r]$0$;
node[right of=t]$1$;
node[right of=2]$0$;
node[right of=3]$2$;
node[right of=4]$0$;
node[right of=5]$1$;
node[right of=6]$2$;
node[right of=7]$0$;
node[right of=8]$2$;
node[right of=9]$1$;
node[right of=10]$0$;
node[right of=11]$1$;
node[right of=12]$2$;
endscope
endtikzpicture
captionc0(mod5)
endsubfigure
captiontest 0
endfigure
enddocument

Notice that for some weird reason, vertex t is placed in the same layer as u7, u8, u9, resulting in a lot of edge overlap. Vertex t should have been placed in a new layer, below the layer containing vertices u10, u11, u12. Is there a way I can force this?

According to the Tikz manual chapter 31st, the layered layout algorithm performs the following steps:

1. Cycle removal.


2. Layer assignment (sometimes called node ranking).


3. Crossing minimization (also referred to as node ordering).


4. Node positioning (or coordinate assignment).


5. Edge routing.

Technically I don't need steps 1,2,5 because I already know the layers for each node, and my graph is guaranteed not to contain cycles. I do however need step 3 to determine the ordering of nodes in each layer to minimize crossings, as well as step 4 to determine coordinates.