Make changes to improve runtime of independent set calculation.

indset.py

@@ -2,24 +2,74 @@
 import matplotlib.pyplot as plt
 from random import choice
 
+
+
 def setUtil(graph):
     if graph.number_of_nodes() == 0:#G is empty
         return 0
 
-    #v = any vertex in G
-    v = choice(graph.nodes())
-    neighborhood = graph.copy().neighbors(v) + [v]
-    #print neighborhood
+    v_zero_degree = [v for v in graph.nodes() if graph.degree(v) == 0]
+    #G has a vertex degree 0
+    if len(v_zero_degree) != 0:
+        withoutV = graph.copy()
+        withoutV.remove_node(choice(v_zero_degree))
+        return 1 + setUtil(withoutV)
+
+    v_one_degree = [v for v in graph.nodes() if graph.degree(v) == 1]
+    #G has a vertex degree one
+    if len(v_one_degree) != 0:
+        v = choice(v_one_degree)
+        w = graph.copy().neighbors(v)[0]
+        w_neighborhood = graph.copy().neighbors(w) + [w]
+        withW = graph.copy()
+        withW.remove_nodes_from(w_neighborhood)
+
+        v_neighborhood = graph.copy().neighbors(v) + [v]
+        withV = graph.copy()
+        withV.remove_nodes_from(v_neighborhood)
+
+        return max(1 + setUtil(withV), 1 + setUtil(withW))
+
+
+    v_three_or_more_degree = [v for v in graph.nodes() if graph.degree(v) > 2]
+    #G has a vertex degree >=3
+    if len(v_three_or_more_degree) != 0:
+        v = choice(v_three_or_more_degree)
+        neighborhood = graph.copy().neighbors(v) + [v]
+
+        withV = graph.copy()
+        withV.remove_nodes_from(neighborhood)
 
-    withV = graph.copy()
-    withV.remove_nodes_from(neighborhood)
+        withoutV = graph.copy()
+        withoutV.remove_node(v)
 
-    withoutV = graph.copy()
-    withoutV.remove_node(v)
+        return max(1 + setUtil(withV), setUtil(withoutV)) 
 
-    return max(1 + setUtil(withV), setUtil(withoutV)) 
+    #every vertex in G has degree 2
+    else:
+        v = choice(graph.nodes())
+        #should be exactly two of these
+        u,w = graph.copy().neighbors(v)
+        u_neighborhood = graph.copy().neighbors(u) + [u]
+        v_neighborhood = graph.copy().neighbors(v) + [v]
+        w_neighborhood = graph.copy().neighbors(w) + [w]
+
+        withU = graph.copy()
+        withU.remove_nodes_from(u_neighborhood)
+
+        withV = graph.copy()
+        withV.remove_nodes_from(v_neighborhood)
+
+
+        withW = graph.copy()
+        withW.remove_nodes_from(w_neighborhood)
+
+        return max(1+setUtil(withU), 1+setUtil(withV), 1+setUtil(withW))
 
 G = nx.cycle_graph(5)
 S = nx.strong_product(G, G)
-Q = nx.strong_product(G, S)
-print setUtil(Q)
+
+G2 = nx.cycle_graph(7)
+S2 = nx.strong_product(G2, G2)
+
+print setUtil(S)