Move canonize_colored_graph and save_colored_graph to lib/colored_graphs
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
This commit is contained in:
@@ -1,245 +0,0 @@
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"""Example: colored pentagon reduction on a random 20-vertex triangulation."""
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import base64
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import hashlib
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import json
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from collections import defaultdict
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from pathlib import Path
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from typing import Any, cast, TypedDict, Literal
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from sage.all import graphs, Graph, save, load # type: ignore[attr-defined] # pylint: disable=no-name-in-module
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from lib.tutte_embedding import tutte_embedding
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from lib.planar_embedding import outer_face, get_embedding_from_pos
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DIR = Path(__file__).parent.parent
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PALETTE = ['red', 'blue', 'green', 'yellow']
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VertexColoring = dict[Any, Any]
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class ColoredGraphId(TypedDict):
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"""Canonical id representing a colored graph"""
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graph_id: str
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coloring_id: str
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class Operation(TypedDict):
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"""Information about a change made to a (colored) graph"""
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name: Any
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meta: Any
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source_graph: Graph
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source_canon_id: ColoredGraphId
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result_graph: Graph
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result_coloring: VertexColoring
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result_canon_id: ColoredGraphId
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class CanonicalColoredGraph(TypedDict):
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"""Canonical representation of a colored graph"""
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colored_graph_id: ColoredGraphId
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graph: Graph
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coloring: VertexColoring
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def colored_graph_id_to_string(cid: ColoredGraphId) -> str:
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return f"{cid['graph_id']} {cid['coloring_id']}"
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def op_to_transform_id(op: Operation) -> str:
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return f"{colored_graph_id_to_string(op['source_canon_id'])} -> {colored_graph_id_to_string(op['result_canon_id'])}"
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def operation_sequence_id(ops: list[Operation]) -> str:
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joined = "\n".join(op_to_transform_id(op) for op in ops)
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return hashlib.sha256(joined.encode()).hexdigest()
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def canonize_colored_graph(g: Graph, coloring: VertexColoring) -> tuple[Graph, VertexColoring, ColoredGraphId]:
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"""Return a new canonical graph, new canonical coloring, and a ColoredGraphId without mutating inputs"""
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canonical, cert = cast(
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tuple[Graph, dict[Any, int]],
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g.canonical_label(certificate=True),
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)
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graph_id = base64.urlsafe_b64encode(
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canonical.graph6_string().encode()
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).decode()
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color_seq = [0] * g.order()
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for orig_v, canon_idx in cert.items():
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color_seq[canon_idx] = coloring[orig_v]
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canonical_coloring = {canon_idx: color for canon_idx, color in enumerate(color_seq)}
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coloring_id = base64.urlsafe_b64encode(bytes(color_seq)).decode()
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return canonical, canonical_coloring, ColoredGraphId(graph_id=graph_id, coloring_id=coloring_id)
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def save_colored_graph(g: Graph, coloring: VertexColoring) -> tuple[Graph, VertexColoring, ColoredGraphId]:
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"""
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Canonize g and coloring, save to disk, and return the canonical forms with id.
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If already saved, load and return the cached graph.
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"""
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g_canon, canonical_coloring, cid = canonize_colored_graph(g, coloring)
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out_dir = DIR / "data" / "graphs" / cid['graph_id'] / cid['coloring_id']
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if (out_dir / "graph.sobj").exists():
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g_canon = cast(Graph, load(str(out_dir / 'graph')))
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return g_canon, canonical_coloring, cid
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g_canon.is_planar(set_embedding=True, set_pos=True)
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vertex_colors: defaultdict[str, list[Any]] = defaultdict(list)
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for v, c in canonical_coloring.items():
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vertex_colors[PALETTE[c]].append(v)
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out_dir.mkdir(parents=True, exist_ok=True)
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g_canon.plot(
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vertex_colors=dict(vertex_colors),
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title=f"graph: {cid['graph_id']} coloring: {cid['coloring_id']}",
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).save(out_dir / 'graph.png')
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save(g_canon, str(out_dir / 'graph'))
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return g_canon, canonical_coloring, cid
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def _neighbors_form_cycle(g: Graph, v: Any) -> bool:
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"""Return True if the neighbors of v induce a cycle in g."""
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return bool(cast(Graph, g.subgraph(g.neighbors(v))).is_cycle())
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class PluckMeta(TypedDict):
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"""Meta information about the pluck operation"""
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v0: Any
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class PluckOperation(Operation):
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"""Info about an operation in which a vertex v0 and its incident edges is removed from G"""
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name: Literal['pluck']
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meta: PluckMeta
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def pluck(g: Graph, coloring: VertexColoring, v0: Any) -> tuple[Graph, VertexColoring]:
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"""Delete v0 and all its incident edges from g"""
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g_prime = g.copy()
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g_prime.delete_vertex(v0)
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if (pos := g.get_pos()) is not None:
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g_prime.set_pos({v: p for v, p in pos.items() if v != v0})
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g_prime.set_embedding(get_embedding_from_pos(g_prime))
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coloring_prime = coloring.copy()
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del coloring_prime[v0]
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return g_prime, coloring_prime
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class SquishMeta(TypedDict):
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"""Meta information about the squish operation"""
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v0: Any
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v_merged: list[Any]
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class SquishOperation(Operation):
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"""
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Info about an operation in which two same colored neighbors of a vertex v0 are merged
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into v0
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"""
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name: Literal['squish']
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meta: SquishMeta
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def squish(g: Graph, coloring: VertexColoring, v0: Any) -> tuple[Graph, VertexColoring, Any, Any]:
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"""
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Contract two same-colored neighbors of v0 into v0 and return a new valid
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coloring along with the new graph.
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NOTE: assumes g is a maximal planar graph
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"""
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neighbor_by_color: defaultdict[Any, list[Any]] = defaultdict(list)
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for v in g.neighbors(v0):
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neighbor_by_color[coloring[v]].append(v)
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v1, v2 = next(
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(vs[0], vs[1]) for vs in neighbor_by_color.values() if len(vs) >= 2
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)
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g_prime = g.copy()
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g_prime.merge_vertices([v0, v1, v2])
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if (pos := g.get_pos()) is not None:
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g_prime.set_pos({v: p for v, p in pos.items() if v not in (v1, v2)})
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g_prime.set_embedding(get_embedding_from_pos(g_prime))
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coloring_prime = {v: c for v, c in coloring.items() if v not in (v1, v2)}
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coloring_prime[v0] = coloring[v1]
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return g_prime, coloring_prime, v1, v2
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ReduceOperation = SquishOperation | PluckOperation
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def reduce(
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g: Graph,
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coloring: VertexColoring,
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source_canon_id: ColoredGraphId,
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op_sequence: list[ReduceOperation] | None = None,
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) -> list[ReduceOperation]:
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"""Repeatedly apply pluck/squish reductions until no candidates remain."""
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if op_sequence is None:
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op_sequence = []
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print(f"Coloring: {coloring}")
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degree_4_candidates: list[Any] = []
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degree_5_candidates: list[Any] = []
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for v in g.vertices():
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if g.degree(v) == 3 and _neighbors_form_cycle(g, v):
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result_graph, result_coloring = pluck(g, coloring, v)
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print(f"\nG' (after pluck v0={v}): {result_graph.order()} vertices, {result_graph.size()} edges")
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_, _, result_canon_id = save_colored_graph(result_graph, result_coloring)
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op_sequence.append(PluckOperation(name='pluck', meta=PluckMeta(v0=v), source_graph=g, source_canon_id=source_canon_id, result_graph=result_graph, result_coloring=result_coloring, result_canon_id=result_canon_id))
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return reduce(result_graph, result_coloring, result_canon_id, op_sequence)
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if g.degree(v) == 4 and _neighbors_form_cycle(g, v):
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degree_4_candidates.append(v)
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elif g.degree(v) == 5 and _neighbors_form_cycle(g, v):
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degree_5_candidates.append(v)
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if degree_4_candidates:
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v0 = degree_4_candidates[0]
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result_graph, result_coloring, v1, v2 = squish(g, coloring, v0)
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print(f"Shared-color neighbors: v1={v1}, v2={v2} (color {coloring[v1]})")
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print(f"\nG' (after squish v0={v0}): {result_graph.order()} vertices, {result_graph.size()} edges")
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_, _, result_canon_id = save_colored_graph(result_graph, result_coloring)
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op_sequence.append(SquishOperation(name='squish', meta=SquishMeta(v0=v0, v_merged=[v1, v2]), source_graph=g, source_canon_id=source_canon_id, result_graph=result_graph, result_coloring=result_coloring, result_canon_id=result_canon_id))
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return reduce(result_graph, result_coloring, result_canon_id, op_sequence)
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if degree_5_candidates:
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v0 = degree_5_candidates[0]
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result_graph, result_coloring, v1, v2 = squish(g, coloring, v0)
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print(f"Shared-color neighbors: v1={v1}, v2={v2} (color {coloring[v1]})")
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print(f"\nG' (after squish v0={v0}): {result_graph.order()} vertices, {result_graph.size()} edges")
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_, _, result_canon_id = save_colored_graph(result_graph, result_coloring)
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op_sequence.append(SquishOperation(name='squish', meta=SquishMeta(v0=v0, v_merged=[v1, v2]), source_graph=g, source_canon_id=source_canon_id, result_graph=result_graph, result_coloring=result_coloring, result_canon_id=result_canon_id))
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return reduce(result_graph, result_coloring, result_canon_id, op_sequence)
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print("DONE")
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return op_sequence
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G = next(graphs.planar_graphs(20, minimum_degree=5))
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print(f"G: {G.order()} vertices, {G.size()} edges")
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print(f"Degree sequence: {sorted(G.degree_sequence(), reverse=True)}")
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starting_coloring_classes = G.coloring()
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starting_coloring = {v: i for i, cls in enumerate(starting_coloring_classes) for v in cls}
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_, _, initial_canon_id = save_colored_graph(G, starting_coloring)
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G.is_planar(set_embedding=True, set_pos=True)
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def strip_graphs(obj: Any) -> Any:
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if isinstance(obj, dict):
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return {k: strip_graphs(v) for k, v in obj.items() if not isinstance(v, Graph)}
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if isinstance(obj, list):
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return [strip_graphs(v) for v in obj]
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return obj
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def plot_to_data_uri(g: Graph, coloring: VertexColoring) -> str:
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import tempfile
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vertex_colors: defaultdict[str, list[Any]] = defaultdict(list)
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for v, c in coloring.items():
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vertex_colors[PALETTE[c]].append(v)
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if g.get_pos() is None:
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g.is_planar(set_embedding=True, set_pos=True)
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g.set_pos(tutte_embedding(g, outer_face(g)))
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with tempfile.NamedTemporaryFile(suffix='.png', delete=True) as f:
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g.plot(vertex_colors=dict(vertex_colors)).save(f.name)
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png_bytes = Path(f.name).read_bytes()
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return f"data:image/png;base64,{base64.b64encode(png_bytes).decode()}"
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def save_operation_sequence(op_sequence: list[ReduceOperation], g: Graph, coloring: VertexColoring) -> str:
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"""Save op_sequence as JSON and Markdown under data/operations/<seq_id>. Returns the sequence id."""
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op_seq_id = operation_sequence_id(op_sequence)
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op_dir = DIR / "data" / "operations" / op_seq_id
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op_dir.mkdir(parents=True, exist_ok=True)
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(op_dir / "colored_pentagon_contractions.json").write_text(json.dumps(strip_graphs(op_sequence), indent=2))
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md_lines = [f"## start\n\n})"]
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for op in op_sequence:
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meta_json = json.dumps(op['meta'])
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md_lines.append(f"## {op['name']} {meta_json}\n\n})")
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(op_dir / "colored_pentagon_contractions.md").write_text("\n".join(md_lines) + "\n")
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return op_seq_id
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op_sequence = reduce(G, starting_coloring, initial_canon_id)
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print("\nOp sequence:")
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print(json.dumps(strip_graphs(op_sequence), indent=2))
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save_operation_sequence(op_sequence, G, starting_coloring)
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@@ -0,0 +1,60 @@
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"""Utilities for canonizing and saving colored graphs."""
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import base64
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from collections import defaultdict
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from pathlib import Path
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from typing import Any, cast, TypedDict
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from sage.all import Graph, save, load # type: ignore[attr-defined] # pylint: disable=no-name-in-module
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DIR = Path(__file__).parent.parent
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PALETTE = ['red', 'blue', 'green', 'yellow']
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VertexColoring = dict[Any, Any]
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class ColoredGraphId(TypedDict):
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"""Canonical id representing a colored graph"""
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graph_id: str
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coloring_id: str
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def canonize_colored_graph(g: Graph, coloring: VertexColoring) -> tuple[Graph, VertexColoring, ColoredGraphId]:
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"""Return a new canonical graph, new canonical coloring, and a ColoredGraphId without mutating inputs"""
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canonical, cert = cast(
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tuple[Graph, dict[Any, int]],
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g.canonical_label(certificate=True),
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)
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graph_id = base64.urlsafe_b64encode(
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canonical.graph6_string().encode()
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).decode()
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color_seq = [0] * g.order()
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for orig_v, canon_idx in cert.items():
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color_seq[canon_idx] = coloring[orig_v]
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canonical_coloring = {canon_idx: color for canon_idx, color in enumerate(color_seq)}
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coloring_id = base64.urlsafe_b64encode(bytes(color_seq)).decode()
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return canonical, canonical_coloring, ColoredGraphId(graph_id=graph_id, coloring_id=coloring_id)
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def save_colored_graph(g: Graph, coloring: VertexColoring) -> tuple[Graph, VertexColoring, ColoredGraphId]:
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"""
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Canonize g and coloring, save to disk, and return the canonical forms with id.
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If already saved, load and return the cached graph.
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"""
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g_canon, canonical_coloring, cid = canonize_colored_graph(g, coloring)
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out_dir = DIR / "data" / "graphs" / cid['graph_id'] / cid['coloring_id']
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if (out_dir / "graph.sobj").exists():
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g_canon = cast(Graph, load(str(out_dir / 'graph')))
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return g_canon, canonical_coloring, cid
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g_canon.is_planar(set_embedding=True, set_pos=True)
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vertex_colors: defaultdict[str, list[Any]] = defaultdict(list)
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for v, c in canonical_coloring.items():
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vertex_colors[PALETTE[c]].append(v)
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out_dir.mkdir(parents=True, exist_ok=True)
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g_canon.plot(
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vertex_colors=dict(vertex_colors),
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title=f"graph: {cid['graph_id']} coloring: {cid['coloring_id']}",
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).save(out_dir / 'graph.png')
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save(g_canon, str(out_dir / 'graph'))
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return g_canon, canonical_coloring, cid
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