Merge remote-tracking branch 'origin/main'

Author: SebVde

bafna_fvs.py

@@ -0,0 +1,67 @@
+import networkx as nx
+
+
+def cleanup(G):
+    new_G = G.copy()
+    while True:
+        to_remove = [node for node in new_G.nodes if new_G.degree(node) <= 1]
+        if len(to_remove) == 0:
+            break
+        new_G.remove_nodes_from(to_remove)
+
+    return new_G
+
+
+def find_semidisjoint_cycle(G):
+    for cycle in nx.cycle_basis(G):
+        cnt = 0
+        for node in cycle:
+            if G.degree(node) != 2:
+                cnt += 1
+            if cnt > 1:
+                break
+        if cnt <= 1:
+            return cycle
+    return None
+
+
+def get_fvs(og_G):
+    F = set()
+    i = 0
+    stack = []
+    G = og_G.copy()
+
+    while len(G.nodes) > 0:
+        i += 1
+        sd_cycle = find_semidisjoint_cycle(G)
+        if sd_cycle is not None:
+            for node in sd_cycle:
+                G.node[node]["weight"] = 0.0
+
+        else:
+            gamma = min(1 / (G.degree(node) - 1) for node in G.nodes)
+            for node in G.nodes:
+                G.nodes[node]["weight"] -= gamma * (G.degree(node) - 1)
+
+        to_remove = [node for node in G.nodes if G.nodes[node]["weight"] == 0.0]
+        F.update(to_remove)
+        G.remove_nodes_from(to_remove)
+        stack.extend(to_remove)
+        G = cleanup(G)
+
+    while len(stack) > 0:
+        node = stack.pop()
+        sg = nx.subgraph(og_G, og_G.nodes - (F - {node}))
+        if nx.is_forest(sg):
+            F.remove(node)
+
+    return F
+
+
+def get_decycling_number_2_approx(G):
+    clean_G = cleanup(G)
+    for node in clean_G.nodes:
+        clean_G.nodes[node]["weight"] = 1.0
+
+    fvs = get_fvs(clean_G)
+    return len(fvs)

requirements.txt

@@ -1,2 +1,3 @@
 networkx==3.5
+numpy==2.3.4
 pyvis==0.3.2