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Add outer_face and tutte_embedding for improved graph visualization

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Adds outer face detection via face traversal and signed area, Tutte embedding
for clean planar layouts, and moves g/g_prime/coloring_prime into base Operation
type. Pluck and squish now carry positions and recompute embeddings via is_planar.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-04-21 03:05:18 -04:00
parent 9e4d17bd50
commit 737db34109
1 changed files with 106 additions and 11 deletions
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colored_pentagon_reduction/example.py
+106 -11
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@@ -24,6 +24,9 @@ class Operation(TypedDict):
meta: Any
before: ColoredGraphId
after: ColoredGraphId
g: Graph
g_prime: Graph
coloring_prime: VertexColoring
class CanonicalColoredGraph(TypedDict):
"""Canonical representation of a colored graph"""
@@ -81,6 +84,77 @@ def save_colored_graph(g: Graph, coloring: VertexColoring) -> tuple[Graph, Verte
save(g_canon, str(out_dir / 'graph'))
return g_canon, canonical_coloring, cid
def outer_face(g: Graph) -> list[Any]:
"""Return the vertices of the outer (unbounded) face of g using its planar embedding and positions."""
pos = g.get_pos()
embedding = g._embedding
visited: set[tuple[Any, Any]] = set()
faces: list[list[Any]] = []
for u in g.vertices():
for v in embedding[u]:
if (u, v) not in visited:
face: list[Any] = []
cu, cv = u, v
while (cu, cv) not in visited:
visited.add((cu, cv))
face.append(cu)
neighbors = embedding[cv]
cw = neighbors[(neighbors.index(cu) + 1) % len(neighbors)]
cu, cv = cv, cw
faces.append(face)
def signed_area(face: list[Any]) -> float:
coords = [pos[v] for v in face]
n = len(coords)
return sum(
coords[i][0] * coords[(i + 1) % n][1] - coords[(i + 1) % n][0] * coords[i][1]
for i in range(n)
) / 2
return min(faces, key=signed_area)
def tutte_embedding(g: Graph, outer: list[Any]) -> dict[Any, tuple[float, float]]:
"""Compute a Tutte embedding fixing outer on a convex polygon, solving for inner vertices."""
import math
import numpy as np
outer_set = set(outer)
inner = [v for v in g.vertices() if v not in outer_set]
pos: dict[Any, tuple[float, float]] = {}
for i, v in enumerate(outer):
angle = 2 * math.pi * i / len(outer)
pos[v] = (math.cos(angle), math.sin(angle))
if not inner:
return pos
inner_idx = {v: i for i, v in enumerate(inner)}
n = len(inner)
A = np.zeros((n, n))
bx = np.zeros(n)
by = np.zeros(n)
for i, v in enumerate(inner):
neighbors = g.neighbors(v)
deg = len(neighbors)
A[i, i] = 1.0
for w in neighbors:
if w in inner_idx:
A[i, inner_idx[w]] = -1.0 / deg
else:
bx[i] += pos[w][0] / deg
by[i] += pos[w][1] / deg
x = np.linalg.solve(A, bx)
y = np.linalg.solve(A, by)
for i, v in enumerate(inner):
pos[v] = (float(x[i]), float(y[i]))
return pos
def _neighbors_form_cycle(g: Graph, v: Any) -> bool:
"""Return True if the neighbors of v induce a cycle in g."""
return bool(cast(Graph, g.subgraph(g.neighbors(v))).is_cycle())
@@ -98,6 +172,9 @@ def pluck(g: Graph, coloring: VertexColoring, v0: Any) -> tuple[Graph, VertexCol
"""Delete v0 and all its incident edges from g"""
g_prime = g.copy()
g_prime.delete_vertex(v0)
if (pos := g.get_pos()) is not None:
g_prime.set_pos({v: p for v, p in pos.items() if v != v0})
g_prime.is_planar(set_embedding=True)
coloring_prime = coloring.copy()
del coloring_prime[v0]
return g_prime, coloring_prime
@@ -132,6 +209,9 @@ def squish(g: Graph, coloring: VertexColoring, v0: Any) -> tuple[Graph, VertexCo
g_prime = g.copy()
g_prime.merge_vertices([v0, v1, v2])
if (pos := g.get_pos()) is not None:
g_prime.set_pos({v: p for v, p in pos.items() if v not in (v1, v2)})
g_prime.is_planar(set_embedding=True)
coloring_prime = {v: c for v, c in coloring.items() if v not in (v1, v2)}
coloring_prime[v0] = coloring[v1]
return g_prime, coloring_prime, v1, v2
@@ -159,7 +239,7 @@ def reduce(
g_prime, coloring_prime = pluck(g, coloring, v)
print(f"\nG' (after pluck v0={v}): {g_prime.order()} vertices, {g_prime.size()} edges")
_, _, after_cid = save_colored_graph(g_prime, coloring_prime)
steps.append(PluckOperation(name='pluck', meta=PluckMeta(v0=v), before=before_cid, after=after_cid))
steps.append(PluckOperation(name='pluck', meta=PluckMeta(v0=v), g=g, g_prime=g_prime, coloring_prime=coloring_prime, before=before_cid, after=after_cid))
return reduce(g_prime, coloring_prime, after_cid, steps)
if g.degree(v) == 4 and _neighbors_form_cycle(g, v):
degree_4_candidates.append(v)
@@ -172,7 +252,7 @@ def reduce(
print(f"Shared-color neighbors: v1={v1}, v2={v2} (color {coloring[v1]})")
print(f"\nG' (after squish v0={v0}): {g_prime.order()} vertices, {g_prime.size()} edges")
_, _, after_cid = save_colored_graph(g_prime, coloring_prime)
steps.append(SquishOperation(name='squish', meta=SquishMeta(v0=v0, v_merged=[v1, v2]), before=before_cid, after=after_cid))
steps.append(SquishOperation(name='squish', meta=SquishMeta(v0=v0, v_merged=[v1, v2]), g=g, g_prime=g_prime, coloring_prime=coloring_prime, before=before_cid, after=after_cid))
return reduce(g_prime, coloring_prime, after_cid, steps)
if degree_5_candidates:
@@ -181,7 +261,7 @@ def reduce(
print(f"Shared-color neighbors: v1={v1}, v2={v2} (color {coloring[v1]})")
print(f"\nG' (after squish v0={v0}): {g_prime.order()} vertices, {g_prime.size()} edges")
_, _, after_cid = save_colored_graph(g_prime, coloring_prime)
steps.append(SquishOperation(name='squish', meta=SquishMeta(v0=v0, v_merged=[v1, v2]), before=before_cid, after=after_cid))
steps.append(SquishOperation(name='squish', meta=SquishMeta(v0=v0, v_merged=[v1, v2]), g=g, g_prime=g_prime, coloring_prime=coloring_prime, before=before_cid, after=after_cid))
return reduce(g_prime, coloring_prime, after_cid, steps)
print("DONE")
@@ -194,24 +274,39 @@ print(f"Degree sequence: {sorted(G.degree_sequence(), reverse=True)}")
starting_coloring_classes = G.coloring()
starting_coloring = {v: i for i, cls in enumerate(starting_coloring_classes) for v in cls}
_, _, initial_cid = save_colored_graph(G, starting_coloring)
G.is_planar(set_embedding=True, set_pos=True)
steps = reduce(G, starting_coloring, initial_cid)
def strip_graphs(obj: Any) -> Any:
if isinstance(obj, dict):
return {k: strip_graphs(v) for k, v in obj.items() if not isinstance(v, Graph)}
if isinstance(obj, list):
return [strip_graphs(v) for v in obj]
return obj
print("\nSteps:")
print(json.dumps(steps, indent=2))
print(json.dumps(strip_graphs(steps), indent=2))
op_seq_id = operation_sequence_id(steps)
op_dir = DIR / "data" / "operations" / op_seq_id
op_dir.mkdir(parents=True, exist_ok=True)
(op_dir / "colored_pentagon_contractions.json").write_text(json.dumps(steps, indent=2))
(op_dir / "colored_pentagon_contractions.json").write_text(json.dumps(strip_graphs(steps), indent=2))
def img_data_uri(cid: ColoredGraphId) -> str:
png_bytes = (DIR / "data" / "graphs" / cid['graph_id'] / cid['coloring_id'] / "graph.png").read_bytes()
def plot_to_data_uri(g: Graph, coloring: VertexColoring) -> str:
import tempfile
vertex_colors: defaultdict[str, list[Any]] = defaultdict(list)
for v, c in coloring.items():
vertex_colors[PALETTE[c]].append(v)
if g.get_pos() is None:
g.is_planar(set_embedding=True, set_pos=True)
g.set_pos(tutte_embedding(g, outer_face(g)))
with tempfile.NamedTemporaryFile(suffix='.png', delete=True) as f:
g.plot(vertex_colors=dict(vertex_colors)).save(f.name)
png_bytes = Path(f.name).read_bytes()
return f"data:image/png;base64,{base64.b64encode(png_bytes).decode()}"
md_lines = [f"## start\n\n![start]({img_data_uri(steps[0]['before'])})"]
md_lines = [f"## start\n\n![start]({plot_to_data_uri(G, starting_coloring)})"]
for step in steps:
b = step['before']
a = step['after']
meta_json = json.dumps(step['meta'])
md_lines.append(f"## {step['name']} {meta_json}\n\n![b]({img_data_uri(a)})")
md_lines.append(f"## {step['name']} {meta_json}\n\n![b]({plot_to_data_uri(step['g_prime'], step['coloring_prime'])})")
(op_dir / "colored_pentagon_contractions.md").write_text("\n".join(md_lines) + "\n")