feat: combine layouts to simplify graph

misc/all-graph/04-combine_layout.py

@@ -0,0 +1,113 @@
+#!/usr/bin/env python3
+
+import igraph as ig
+
+
+def split_layer(graph: ig.Graph, step_a: int, step_b: int) -> tuple[list[set[int]], list[set[int]]]:
+
+    def extend_from(node: ig.Vertex) -> tuple[set[ig.Vertex], set[ig.Vertex]]:
+        assert node['step'] == step_a
+
+        scan_a2b = True
+        union_a, union_b = set(), set()
+        curr_set, next_set = set([node]), set()
+
+        while curr_set:
+            for layout in curr_set:
+                for neigh in layout.neighbors():
+                    if scan_a2b and neigh['step'] == step_b and neigh not in union_b:
+                        next_set.add(neigh)
+                    elif not scan_a2b and neigh['step'] == step_a and neigh not in union_a:
+                        next_set.add(neigh)
+
+            union_a.update(curr_set if scan_a2b else next_set)
+            union_b.update(next_set if scan_a2b else curr_set)
+            scan_a2b = not scan_a2b
+            curr_set = next_set
+            next_set = set()
+
+        return union_a, union_b
+
+    assert step_a + 1 == step_b
+
+    layer_a = set(x for x in graph.vs if x['step'] == step_a)
+    layer_b = set(x for x in graph.vs if x['step'] == step_b)
+    layer_num_a, layer_num_b = len(layer_a), len(layer_b)
+    assert layer_num_a > 0 and layer_num_b > 0
+
+    data_a: list[set[int]] = []
+    data_b: list[set[int]] = []
+    while layer_a:
+        # TODO: maybe we should combine all union_a when union_b is empty
+        union_a, union_b = extend_from(layer_a.pop())
+        layer_a -= union_a
+        layer_b -= union_b
+        data_a.append(set(x.index for x in union_a))
+        data_b.append(set(x.index for x in union_b))
+
+    assert len(layer_a) == 0 and len(layer_b) == 0
+    assert sum(len(x) for x in data_a) == layer_num_a
+    assert sum(len(x) for x in data_b) == layer_num_b
+    return data_a, [x for x in data_b if x]
+
+
+def build_multi_set(unions_a: list[set[int]], unions_b: list[set[int]]) -> list[set[int]]:
+    assert set(y for x in unions_a for y in x) == set(y for x in unions_b for y in x)
+
+    release = []
+    for curr in unions_a:
+        for other in unions_b:
+            mid = curr.intersection(other)
+            if mid:
+                release.append(mid)
+                curr -= mid
+                other -= mid
+        assert len(curr) == 0
+
+    assert set(len(x) for x in unions_a) == {0}
+    assert set(len(x) for x in unions_b) == {0}
+    return release
+
+
+def do_split(file: str) -> ig.Graph:
+    g = ig.Graph.Read_Pickle(file)
+    max_step = max(x['step'] for x in g.vs)
+
+    layer_data = [[] for _ in range(max_step + 1)]
+    layer_data[0].append([set(x.index for x in g.vs if x['step'] == 0)])
+    for step in range(0, max_step):
+        data_a, data_b = split_layer(g, step, step + 1)
+        layer_data[step].append(data_a)
+        layer_data[step + 1].append(data_b)
+    layer_data[max_step].append([set(x.index for x in g.vs if x['step'] == max_step)])
+
+    assert len(layer_data) == max_step + 1
+    assert set(len(x) for x in layer_data) == {2}
+
+    unions = {}
+    for step in range(0, max_step + 1):
+        layer_unions = build_multi_set(layer_data[step][0], layer_data[step][1])
+        for union in layer_unions:
+            assert len(set(g.vs[x]['step'] for x in union)) == 1
+            codes = [g.vs[x]['code'] for x in union]
+            unions[min(codes)] = union
+
+    assert sorted(y for x in unions.values() for y in x) == list(range(g.vcount()))
+
+    combine_info = [-1 for _ in range(g.vcount())]
+    for index, key in enumerate(sorted(unions)):
+        for x in unions[key]:
+            combine_info[x] = index
+
+    assert len(combine_info) == g.vcount()
+    assert set(combine_info) == set(range(len(unions)))
+
+    g.contract_vertices(combine_info, combine_attrs={'step': 'first', 'code': list})
+    assert set(x.is_loop() for x in g.es) == {False}
+    g.simplify(multiple=True)
+    return g
+
+
+if __name__ == "__main__":
+    g_release = do_split('output-ig/1-00M-000Y_DAA7F30.pkl')
+    g_release.write_pickle('1-00M-000Y_DAA7F30-combined.pkl')