Mercurial > public > think_complexity
changeset 25:a46783561538
Implement Floyd-Warshall all pairs shortest path algorithm.
author | Brian Neal <bgneal@gmail.com> |
---|---|
date | Sat, 05 Jan 2013 13:00:07 -0600 |
parents | 5c2c4ce095ef |
children | f6073c187926 |
files | SmallWorldGraph.py ch4ex4.py |
diffstat | 2 files changed, 57 insertions(+), 7 deletions(-) [+] |
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--- a/SmallWorldGraph.py Thu Jan 03 18:41:13 2013 -0600 +++ b/SmallWorldGraph.py Sat Jan 05 13:00:07 2013 -0600 @@ -127,12 +127,42 @@ queue.append(w) sort_flag = True + def all_pairs_floyd_warshall(self): + """Finds the shortest paths between all pairs of vertices using the + Floyd-Warshall algorithm. + + http://en.wikipedia.org/wiki/Floyd-Warshall_algorithm + + """ + vertices = self.vertices() + dist = {} + for i in vertices: + for j in vertices: + if i is j: + dist[i, j] = 0.0 + else: + e = self.get_edge(i, j) + dist[i, j] = e.length if e else INFINITY + + for k in vertices: + for i in vertices: + for j in vertices: + d_ik = dist[i, k] + d_kj = dist[k, j] + new_cost = d_ik + d_kj + if new_cost < dist[i, j]: + dist[i, j] = new_cost + + return dist + def big_l(self): """Computes the "big-L" value for the graph as per Watts & Strogatz. big_l() is defined as the number of edges in the shortest path between two vertices, averaged over all vertices. + Uses the shortest_path_tree() method, called once for every node. + """ d = {} for v in self.vertices(): @@ -143,3 +173,20 @@ if len(d): return sum(d.values()) / float(len(d)) return 0.0 + + def big_l2(self): + """Computes the "big-L" value for the graph as per Watts & Strogatz. + + big_l() is defined as the number of edges in the shortest path between + two vertices, averaged over all vertices. + + Uses the all_pairs_floyd_warshall() method. + + """ + dist = self.all_pairs_floyd_warshall() + vertices = self.vertices() + result = [dist[i, j] for i in vertices for j in vertices if i is not j] + + if len(result): + return sum(result) / float(len(result)) + return 0.0
--- a/ch4ex4.py Thu Jan 03 18:41:13 2013 -0600 +++ b/ch4ex4.py Sat Jan 05 13:00:07 2013 -0600 @@ -5,14 +5,13 @@ for small values of p." """ -import random import matplotlib.pyplot as pyplot from Graph import Vertex from SmallWorldGraph import SmallWorldGraph - -title = 'C(p)/C(0)' +# Use Dijkstra or Floyd-Warshall to compute L +DIJKSTRA = False # compute C(0) n = 1000 @@ -20,12 +19,11 @@ vs = [Vertex(str(i)) for i in range(n)] g = SmallWorldGraph(vs, k, 0.0) c0 = g.clustering_coefficient() -l0 = g.big_l() +l0 = g.big_l() if DIJKSTRA else g.big_l2() print 'c0 =', c0, 'l0 =', l0 # compute data -p_vals = [# 0, - 0.0001, 0.0002, 0.0004, # 0.0006, 0.0008, +p_vals = [0.0001, 0.0002, 0.0004, # 0.0006, 0.0008, 0.001, 0.002, 0.004, # 0.006, 0.008, 0.01, 0.02, 0.04, # 0.06, 0.08, 0.1, 0.2, 0.4, # 0.6, 0.8, @@ -36,7 +34,12 @@ for p in p_vals: g = SmallWorldGraph(vs, k, p) c_vals.append(g.clustering_coefficient() / c0) - l_vals.append(g.big_l() / l0) + l = g.big_l() if DIJKSTRA else g.big_l2() + l_vals.append(l / l0) + +p_vals.insert(0, 0.0) +c_vals.insert(0, 1.0) +l_vals.insert(0, 1.0) # plot graph pyplot.clf()