1 PROCEDURE (G: reduced graph, W:positive integer)
 2 Let R(v) be a set of v
 3 Let i be integer
 4 Let U be an empty set
 5 Let i be integer and set i = 0
 6 Let Li be layer i
 7
 8 //Step 1: assign integer labels to vertices.
 9 CALL LabelVertices with G RETURN a set of labelled vertices U
10
11 //Step 2: Assign labelled vertices into layers.
12 //starts from bottom and head to the top
13 //assign all sinks to layer(s)
14 FOR each u in U
15     IF u is a sink
16       Add u to set Li
17       Remove u from U
18       //if the layer i is full
19       //assign vertices to the next layer
20       IF Size(Li) >= W
21           Increment i by 1
22       ENDIF
23     ENDIF
24 END LOOP
25
26 WHILE U not empty
27     //Find a set R of vertices that are not assigned
28     //to a layer yet
29     Call findUnassignedLayeredVertices with G, U return R
30     Sort set R based on the vertex labels
31     IF R is empty THEN
32       Increment i by 1 // next layer
33     ELSE
34       FOR each v in R
35         Add v to Li
36         IF Size(Li) THEN
37           Increment i by 1
38         ENDIF
39       END LOOP
40     ENDIF
41 ENDWHILE
42 END PROCEDURE