1. G <- the complete undirected graph
2. for d = 0, 1, 2, … while some node has > d neighbors
3. adj <- the neighbors in G, fixed for this depth
4. for each adjacent pair (x, y)
5. for each S of size d from adj(x) \ {y} or adj(y) \ {x}
6. p <- test(x, y | S)
7. if p > α: mark x – y, add S to sepset(x, y), keep the largest p as p(x, y)
8. remove the marked edges from G
9. for each unshielded triple x – y – z, highest p(x, z) first
10. if y ∉ sepset(x, z) and neither y -> x nor y -> z
11. orient x -> y <- z
12. apply Meek's rules R1–R3 until nothing changes

Solid ring: the pair tested. Dashed ring: its conditioning set, or the middle of a triple. Faint edge: marked, removed when the depth ends.

Row i, column j is the mark at i on the edge i – j: a bar for a tail, a triangle for an arrowhead; amber undirected, graphite directed.

1. G <- the complete undirected graph
2. for d = 0, 1, 2, … while some node has > d neighbors
3. adj <- the neighbors in G, fixed for this depth
4. for each adjacent pair (x, y)
5. for each S of size d from adj(x) \ {y} or adj(y) \ {x}
6. p <- test(x, y | S)
7. if p > α: mark x – y, add S to sepset(x, y), keep the largest p as p(x, y)
8. remove the marked edges from G
9. for each unshielded triple x – y – z, highest p(x, z) first
10. if y ∉ sepset(x, z) and neither y -> x nor y -> z
11. orient x -> y <- z
12. apply Meek's rules R1–R3 until nothing changes

Row i, column j is the mark at i on the edge i – j: a bar for a tail, a triangle for an arrowhead; amber undirected, graphite directed. Faint cells are marked at this depth.