Merge pull request #10 from SebVde/bar_yehuda_fvs

Bar yehuda fvs

Author: SebVde

bar_yehuda_fvs.py

@@ -0,0 +1,108 @@
+import networkx as nx
+from collections import deque
+
+
+def dfs_construct(G, H, v, visited, edges_visited):
+    visited.add(v)
+    for u in G.neighbors(v):
+        edge = (min(v, u), max(v, u))
+        if edge in edges_visited:
+            continue
+
+        edges_visited.add(edge)
+        deg_u = H.degree[u] if u in H else 0
+        deg_v = H.degree[v] if v in H else 0
+
+        if deg_u < 3 and deg_v < 3:
+            H.add_edge(u, v)
+        if u not in visited:
+            dfs_construct(G, H, u, visited, edges_visited)
+
+
+def find_maximal_2_3_subgraph(G):
+    H = nx.Graph()
+    visited = set()
+    edges_visited = set()
+    for node in G.nodes:
+        if node not in visited:
+            dfs_construct(G, H, node, visited, edges_visited)
+
+    to_remove = {n for n in H.nodes if H.degree(n) < 2}
+    while len(to_remove) > 0:
+        v = to_remove.pop()
+        if v not in H:
+            continue
+
+        nb = set(H.neighbors(v))
+        H.remove_node(v)
+        for u in nb:
+            if u in H and H.degree[u] < 2:
+                to_remove.add(u)
+
+    return H
+
+
+def cycle_exists_with_node(G, n):
+    queue = deque()
+    queue.append((n, None))
+    visited = set()
+    visited.add(n)
+
+    while queue:
+        current, parent = queue.popleft()
+        for nb in G.neighbors(current):
+            if nb == parent:
+                continue
+
+            if nb == n:
+                return True
+
+            if nb not in visited:
+                visited.add(nb)
+                queue.append((nb, current))
+
+    return False
+
+
+def get_critical_linkpoints(G, H):
+    linkpoints = {n for n in H.nodes if H.degree(n) == 2}
+    critical_linkpoints = set()
+
+    for n in linkpoints:
+        sg = nx.subgraph(G, set(G.nodes) - (set(H.nodes) - {n}))
+        if cycle_exists_with_node(sg, n):
+            critical_linkpoints.add(n)
+
+    return critical_linkpoints
+
+
+def is_cycle(G):
+    return all(G.degree(n) == 2 for n in G.nodes)
+
+
+def get_set_covering_cycles(H, X, Y):
+    sg = nx.subgraph(H, set(H.nodes) - X - Y)
+    cover_set = set()
+
+    for comp in nx.connected_components(sg):
+        comp_sg = nx.subgraph(sg, comp)
+        if is_cycle(comp_sg):
+            cover_set.add(next(iter(comp)))
+
+    return cover_set
+
+
+def subG_2_3(G):
+    # Complexité pas linéaire à cause de get_critical_linkpoints
+    if nx.is_forest(G):
+        return set()
+
+    H = find_maximal_2_3_subgraph(G)
+    X = get_critical_linkpoints(G, H)
+    Y = {n for n in H.nodes if H.degree(n) >= 3}
+    W = get_set_covering_cycles(H, X, Y)
+    return X | Y | W
+
+
+def get_decycling_number_bar_yehuda(G):
+    return len(subG_2_3(G))