kgully
Reputation: 662
Find shortest path to one of many nodes with attribute
I have a networkx graph representing the minimum spanning tree of roughly 1 million objects (vertices). I am wondering if there is an efficient way to find the shortest path between a given vertex and one of many other vertices.
Here is an example graph with a smaller number of vertices (110)
nodes = [(0.0, {'label': 2}) ,
(1.0, {'label': 2}) ,
(2.0, {'label': 0}) ,
(3.0, {'label': 2}) ,
(4.0, {'label': 2}) ,
(5.0, {'label': 0}) ,
(6.0, {'label': 0}) ,
(7.0, {'label': 2}) ,
(8.0, {'label': 2}) ,
(9.0, {'label': 1}) ,
(10.0, {'label': 0}) ,
(11.0, {'label': 1}) ,
(12.0, {'label': 1}) ,
(13.0, {'label': 0}) ,
(14.0, {'label': 1}) ,
(15.0, {'label': 2}) ,
(16.0, {'label': 1}) ,
(17.0, {'label': 1}) ,
(18.0, {'label': 2}) ,
(19.0, {'label': 2}) ,
(20.0, {'label': 0}) ,
(21.0, {'label': 1}) ,
(22.0, {'label': 1}) ,
(23.0, {'label': 0}) ,
(24.0, {'label': 1}) ,
(25.0, {'label': 2}) ,
(26.0, {'label': 0}) ,
(27.0, {'label': 0}) ,
(28.0, {'label': 1}) ,
(29.0, {'label': 0}) ,
(30.0, {'label': 2}) ,
(31.0, {'label': 1}) ,
(32.0, {'label': 2}) ,
(33.0, {'label': 1}) ,
(34.0, {'label': 1}) ,
(35.0, {'label': 1}) ,
(36.0, {'label': 1}) ,
(37.0, {'label': 2}) ,
(38.0, {'label': 0}) ,
(39.0, {'label': 0}) ,
(40.0, {'label': 2}) ,
(41.0, {'label': 0}) ,
(42.0, {'label': 1}) ,
(43.0, {'label': 0}) ,
(44.0, {'label': 0}) ,
(45.0, {'label': 2}) ,
(46.0, {'label': 0}) ,
(47.0, {'label': 2}) ,
(48.0, {'label': 0}) ,
(49.0, {'label': 1}) ,
(50.0, {'label': 0}) ,
(51.0, {'label': 1}) ,
(52.0, {'label': 2}) ,
(53.0, {'label': 0}) ,
(54.0, {'label': 1}) ,
(55.0, {'label': 1}) ,
(56.0, {'label': 2}) ,
(57.0, {'label': 1}) ,
(58.0, {'label': 1}) ,
(59.0, {'label': 0}) ,
(60.0, {'label': 2}) ,
(61.0, {'label': 1}) ,
(62.0, {'label': 1}) ,
(63.0, {'label': 2}) ,
(64.0, {'label': 0}) ,
(65.0, {'label': 0}) ,
(66.0, {'label': 0}) ,
(67.0, {'label': 0}) ,
(68.0, {'label': 1}) ,
(69.0, {'label': 2}) ,
(70.0, {'label': 0}) ,
(71.0, {'label': 1}) ,
(72.0, {'label': 0}) ,
(73.0, {'label': 2}) ,
(74.0, {'label': 0}) ,
(75.0, {'label': 1}) ,
(76.0, {'label': 1}) ,
(77.0, {'label': 0}) ,
(78.0, {'label': 2}) ,
(79.0, {'label': 2}) ,
(80.0, {'label': 2}) ,
(81.0, {'label': 1}) ,
(82.0, {'label': 2}) ,
(83.0, {'label': 2}) ,
(84.0, {'label': 1}) ,
(85.0, {'label': 0}) ,
(86.0, {'label': 1}) ,
(87.0, {'label': 2}) ,
(88.0, {'label': 1}) ,
(89.0, {'label': 0}) ,
(90.0, {'label': 0}) ,
(91.0, {'label': 2}) ,
(92.0, {'label': 0}) ,
(93.0, {'label': 1}) ,
(94.0, {'label': 1}) ,
(95.0, {'label': 2}) ,
(96.0, {'label': 2}) ,
(97.0, {'label': 0}) ,
(98.0, {'label': 2}) ,
(99.0, {'label': 2}) ,
(100.0, {'label': -1}) ,
(101.0, {'label': -1}) ,
(102.0, {'label': 1}) ,
(103.0, {'label': -1}) ,
(104.0, {'label': -1}) ,
(105.0, {'label': -1}) ,
(106.0, {'label': -1}) ,
(107.0, {'label': 1}) ,
(108.0, {'label': 0}) ,
(109.0, {'label': -1})]
edges = [(0.0, 25.0, {'weight': 1.3788141613435239}) ,
(0.0, 15.0, {'weight': 1.1948288781935414}) ,
(1.0, 99.0, {'weight': 2.1024875417678257}) ,
(1.0, 52.0, {'weight': 1.5298566582843918}) ,
(2.0, 59.0, {'weight': 1.2222170767316791}) ,
(3.0, 96.0, {'weight': 0.77235026806254947}) ,
(3.0, 98.0, {'weight': 0.75540026318653475}) ,
(3.0, 83.0, {'weight': 0.63745598060956865}) ,
(4.0, 8.0, {'weight': 1.1460983565815646}) ,
(5.0, 39.0, {'weight': 0.57882005244148982}) ,
(6.0, 27.0, {'weight': 0.77903808587705414}) ,
(6.0, 38.0, {'weight': 0.87763345274858739}) ,
(7.0, 83.0, {'weight': 1.0592473391743824}) ,
(7.0, 52.0, {'weight': 1.1650063193499598}) ,
(8.0, 18.0, {'weight': 0.62985157194068553}) ,
(8.0, 63.0, {'weight': 0.66061808561292024}) ,
(9.0, 57.0, {'weight': 0.73138423240527128}) ,
(9.0, 14.0, {'weight': 0.68690071596776681}) ,
(10.0, 43.0, {'weight': 1.0938913337235003}) ,
(11.0, 76.0, {'weight': 1.8066534138474315}) ,
(11.0, 22.0, {'weight': 1.5814274601380762}) ,
(12.0, 68.0, {'weight': 0.82964162447510292}) ,
(12.0, 28.0, {'weight': 0.56687613489965616}) ,
(13.0, 41.0, {'weight': 0.67883257822079479}) ,
(13.0, 70.0, {'weight': 0.69594526555853065}) ,
(13.0, 39.0, {'weight': 0.62690609201673064}) ,
(14.0, 42.0, {'weight': 0.51384098628821639}) ,
(15.0, 91.0, {'weight': 0.80363040334950342}) ,
(15.0, 63.0, {'weight': 0.74055429404201112}) ,
(16.0, 75.0, {'weight': 0.89225782872169068}) ,
(16.0, 36.0, {'weight': 0.97796463842832249}) ,
(16.0, 61.0, {'weight': 1.2426060084547763}) ,
(17.0, 24.0, {'weight': 0.48569989925661516}) ,
(17.0, 88.0, {'weight': 0.58411688395739225}) ,
(17.0, 42.0, {'weight': 0.48569989925661516}) ,
(18.0, 19.0, {'weight': 0.73750301595928458}) ,
(18.0, 87.0, {'weight': 0.62985157194068553}) ,
(19.0, 80.0, {'weight': 0.77740196142918039}) ,
(20.0, 53.0, {'weight': 1.5817584651620507}) ,
(21.0, 33.0, {'weight': 1.558483049272277}) ,
(21.0, 35.0, {'weight': 1.022218339608882}) ,
(22.0, 93.0, {'weight': 1.4628634684132413}) ,
(22.0, 101.0, {'weight': 7.494583622053641}) ,
(23.0, 97.0, {'weight': 0.86085201141197409}) ,
(23.0, 90.0, {'weight': 1.4629842172999594}) ,
(23.0, 65.0, {'weight': 0.94746570241498318}) ,
(24.0, 34.0, {'weight': 0.55323853417352553}) ,
(25.0, 104.0, {'weight': 4.9839694794161371}) ,
(26.0, 85.0, {'weight': 1.5024751933287497}) ,
(26.0, 46.0, {'weight': 1.2053565344116006}) ,
(27.0, 72.0, {'weight': 0.72860577250944303}) ,
(27.0, 92.0, {'weight': 0.74002007166874428}) ,
(28.0, 54.0, {'weight': 0.55323853417352553}) ,
(29.0, 50.0, {'weight': 0.81426784351619774}) ,
(30.0, 98.0, {'weight': 0.77235026806254947}) ,
(30.0, 78.0, {'weight': 0.79413937142096647}) ,
(30.0, 95.0, {'weight': 0.78901093530213129}) ,
(31.0, 68.0, {'weight': 0.98851671776185412}) ,
(32.0, 95.0, {'weight': 0.8579399666494596}) ,
(34.0, 54.0, {'weight': 0.55323853417352553}) ,
(34.0, 55.0, {'weight': 0.60906522381767525}) ,
(35.0, 62.0, {'weight': 0.66697239833732958}) ,
(36.0, 93.0, {'weight': 1.2932994772208264}) ,
(37.0, 80.0, {'weight': 0.85527462610640648}) ,
(37.0, 96.0, {'weight': 0.85527462610640648}) ,
(38.0, 46.0, {'weight': 0.95334944284759993}) ,
(39.0, 50.0, {'weight': 0.52028039541706872}) ,
(40.0, 69.0, {'weight': 1.7931323073700682}) ,
(42.0, 62.0, {'weight': 0.51384098628821639}) ,
(42.0, 81.0, {'weight': 0.5466147583189902}) ,
(43.0, 65.0, {'weight': 1.0581157274507453}) ,
(44.0, 108.0, {'weight': 3.0598509599260266}) ,
(44.0, 70.0, {'weight': 1.0805691635112824}) ,
(45.0, 56.0, {'weight': 1.3420236519319457}) ,
(45.0, 79.0, {'weight': 1.6201017824952586}) ,
(46.0, 53.0, {'weight': 1.070516213146298}) ,
(47.0, 78.0, {'weight': 1.2822937333699174}) ,
(47.0, 103.0, {'weight': 3.9053251231648707}) ,
(48.0, 97.0, {'weight': 0.86085201141197409}) ,
(48.0, 67.0, {'weight': 0.75656062694199944}) ,
(49.0, 94.0, {'weight': 1.6216528905308547}) ,
(49.0, 86.0, {'weight': 0.80157999082131093}) ,
(49.0, 62.0, {'weight': 0.7081136236724922}) ,
(51.0, 102.0, {'weight': 1.4704389417937378}) ,
(51.0, 71.0, {'weight': 0.83506431983724716}) ,
(54.0, 75.0, {'weight': 0.70074754481170742}) ,
(55.0, 58.0, {'weight': 0.78571631647476448}) ,
(56.0, 82.0, {'weight': 1.3387438494166808}) ,
(57.0, 84.0, {'weight': 1.558483049272277}) ,
(59.0, 64.0, {'weight': 1.0416266944398496}) ,
(60.0, 98.0, {'weight': 1.2534403896544031}) ,
(63.0, 73.0, {'weight': 0.83646303763566465}) ,
(64.0, 72.0, {'weight': 0.8620326535711742}) ,
(66.0, 77.0, {'weight': 0.79981721989351606}) ,
(67.0, 72.0, {'weight': 0.74002007166874428}) ,
(69.0, 83.0, {'weight': 1.5000235782351021}) ,
(70.0, 77.0, {'weight': 0.75999034076724692}) ,
(71.0, 88.0, {'weight': 0.66450874893016454}) ,
(74.0, 97.0, {'weight': 0.8743417572549379}) ,
(76.0, 107.0, {'weight': 2.0300278349030831}) ,
(77.0, 89.0, {'weight': 0.75999034076724692}) ,
(79.0, 106.0, {'weight': 4.5661761296968333}) ,
(82.0, 95.0, {'weight': 1.083633962514291}) ,
(84.0, 99.0, {'weight': 2.1024875417678257}) ,
(89.0, 92.0, {'weight': 0.75419548272456249}) ,
(100.0, 107.0, {'weight': 2.9259491743365307}) ,
(101.0, 109.0, {'weight': 7.6747981730730297}) ,
(102.0, 108.0, {'weight': 4.3128725576385092}) ,
(104.0, 105.0, {'weight': 7.5515191839631273})]
G2 = nx.Graph()
G2.add_nodes_from(nodes)
G2.add_edges_from(edges)
What I want is "which vertex that has label >= 0 is closest to each of the vertices with label = -1". With a small graph like this, the brute force approach using something like nx.all_pairs_dijkstra_path_length() and then checking the labels works fine, but it doesn't scale to very large graphs. Are there more efficient algorithms, especially if built-in to networkx, that I could use?
UPDATE:
I used the excellent suggestion by Richard and the comment below to write this. What I actually want is an array of labels, which I think made things less messy than Richard alluded to in networkx. The whole relabeling took 45 seconds on a dataset that took an hour to do by brute force!
def relabel(G, indices_to_relabel):
"""
Update the anomaly labels to be the closest cluster.
"""
# Add a "special" node that has zero weight to all the cluster nodes
print('Adding special node')
G.add_node('special', {'label': 'special'})
special_edges = [(n, 'special', {'weight': 0})
for n, ndat in G.nodes_iter(data=True)
if ndat['label'] != 'special' and ndat['label'] >= 0]
G.add_edges_from(special_edges)
print('Calculating path from special node to all other nodes')
paths = nx.shortest_path(G, source='special', target=None, weight='weight')
print('Updating labels')
new_labels = np.array([ndat['label'] for _, ndat in G.nodes_iter(data=True)])
new_labels[indices_to_relabel] = [G.node[paths[n][1]]['label'] for n in indices_to_relabel]
# Clean up
G.remove_node('special')
return new_labels
Upvotes: 3
Views: 2162
Answers (3)
Richard
Reputation: 61499
I don't think there's such an algorithm built into networkx, but it does seem as though it would be sensible to have an algorithm which expands the least-cost path until a condition is reached. However, even though networkx does not include such a capability, it's pretty easy to build an algorithm to do this.
- Call the nodes with
label==-1the source nodes. - Call the node with
label>=0which is closest to a source node its target node. Our goal is to find the target nodes. - Create a new node. This will be the special node.
- Connect all of the potential target nodes to the special node with edges of weight 0.
- For each source node, find the shortest path to the special node. The penultimate node on this path is necessarily a target node and is the closest one to the source node.
- When finished, eliminate the special node and all its connecting edges.
If the number of source nodes is S, this algorithm runs in O(S(|E|+|V| log |V|)) time (assuming the shortest path algorithm is Dijkstra).
(It may be that I've misunderstood whether you want the -1's closest to the >=0's or the >=0's closest to the -1's. If I have, just invert the source/target labeling.)
#!/usr/bin/env python3
import networkx as nx
nodes = [(0.0, {'label': 2}) ,
(1.0, {'label': 2}) ,
(2.0, {'label': 0}) ,
(3.0, {'label': 2}) ,
(4.0, {'label': 2}) ,
(5.0, {'label': 0}) ,
(6.0, {'label': 0}) ,
(7.0, {'label': 2}) ,
(8.0, {'label': 2}) ,
(9.0, {'label': 1}) ,
(10.0, {'label': 0}) ,
(11.0, {'label': 1}) ,
(12.0, {'label': 1}) ,
(13.0, {'label': 0}) ,
(14.0, {'label': 1}) ,
(15.0, {'label': 2}) ,
(16.0, {'label': 1}) ,
(17.0, {'label': 1}) ,
(18.0, {'label': 2}) ,
(19.0, {'label': 2}) ,
(20.0, {'label': 0}) ,
(21.0, {'label': 1}) ,
(22.0, {'label': 1}) ,
(23.0, {'label': 0}) ,
(24.0, {'label': 1}) ,
(25.0, {'label': 2}) ,
(26.0, {'label': 0}) ,
(27.0, {'label': 0}) ,
(28.0, {'label': 1}) ,
(29.0, {'label': 0}) ,
(30.0, {'label': 2}) ,
(31.0, {'label': 1}) ,
(32.0, {'label': 2}) ,
(33.0, {'label': 1}) ,
(34.0, {'label': 1}) ,
(35.0, {'label': 1}) ,
(36.0, {'label': 1}) ,
(37.0, {'label': 2}) ,
(38.0, {'label': 0}) ,
(39.0, {'label': 0}) ,
(40.0, {'label': 2}) ,
(41.0, {'label': 0}) ,
(42.0, {'label': 1}) ,
(43.0, {'label': 0}) ,
(44.0, {'label': 0}) ,
(45.0, {'label': 2}) ,
(46.0, {'label': 0}) ,
(47.0, {'label': 2}) ,
(48.0, {'label': 0}) ,
(49.0, {'label': 1}) ,
(50.0, {'label': 0}) ,
(51.0, {'label': 1}) ,
(52.0, {'label': 2}) ,
(53.0, {'label': 0}) ,
(54.0, {'label': 1}) ,
(55.0, {'label': 1}) ,
(56.0, {'label': 2}) ,
(57.0, {'label': 1}) ,
(58.0, {'label': 1}) ,
(59.0, {'label': 0}) ,
(60.0, {'label': 2}) ,
(61.0, {'label': 1}) ,
(62.0, {'label': 1}) ,
(63.0, {'label': 2}) ,
(64.0, {'label': 0}) ,
(65.0, {'label': 0}) ,
(66.0, {'label': 0}) ,
(67.0, {'label': 0}) ,
(68.0, {'label': 1}) ,
(69.0, {'label': 2}) ,
(70.0, {'label': 0}) ,
(71.0, {'label': 1}) ,
(72.0, {'label': 0}) ,
(73.0, {'label': 2}) ,
(74.0, {'label': 0}) ,
(75.0, {'label': 1}) ,
(76.0, {'label': 1}) ,
(77.0, {'label': 0}) ,
(78.0, {'label': 2}) ,
(79.0, {'label': 2}) ,
(80.0, {'label': 2}) ,
(81.0, {'label': 1}) ,
(82.0, {'label': 2}) ,
(83.0, {'label': 2}) ,
(84.0, {'label': 1}) ,
(85.0, {'label': 0}) ,
(86.0, {'label': 1}) ,
(87.0, {'label': 2}) ,
(88.0, {'label': 1}) ,
(89.0, {'label': 0}) ,
(90.0, {'label': 0}) ,
(91.0, {'label': 2}) ,
(92.0, {'label': 0}) ,
(93.0, {'label': 1}) ,
(94.0, {'label': 1}) ,
(95.0, {'label': 2}) ,
(96.0, {'label': 2}) ,
(97.0, {'label': 0}) ,
(98.0, {'label': 2}) ,
(99.0, {'label': 2}) ,
(100.0, {'label': -1}) ,
(101.0, {'label': -1}) ,
(102.0, {'label': 1}) ,
(103.0, {'label': -1}) ,
(104.0, {'label': -1}) ,
(105.0, {'label': -1}) ,
(106.0, {'label': -1}) ,
(107.0, {'label': 1}) ,
(108.0, {'label': 0}) ,
(109.0, {'label': -1})]
edges = [(0.0, 25.0, {'weight': 1.3788141613435239}) ,
(0.0, 15.0, {'weight': 1.1948288781935414}) ,
(1.0, 99.0, {'weight': 2.1024875417678257}) ,
(1.0, 52.0, {'weight': 1.5298566582843918}) ,
(2.0, 59.0, {'weight': 1.2222170767316791}) ,
(3.0, 96.0, {'weight': 0.77235026806254947}) ,
(3.0, 98.0, {'weight': 0.75540026318653475}) ,
(3.0, 83.0, {'weight': 0.63745598060956865}) ,
(4.0, 8.0, {'weight': 1.1460983565815646}) ,
(5.0, 39.0, {'weight': 0.57882005244148982}) ,
(6.0, 27.0, {'weight': 0.77903808587705414}) ,
(6.0, 38.0, {'weight': 0.87763345274858739}) ,
(7.0, 83.0, {'weight': 1.0592473391743824}) ,
(7.0, 52.0, {'weight': 1.1650063193499598}) ,
(8.0, 18.0, {'weight': 0.62985157194068553}) ,
(8.0, 63.0, {'weight': 0.66061808561292024}) ,
(9.0, 57.0, {'weight': 0.73138423240527128}) ,
(9.0, 14.0, {'weight': 0.68690071596776681}) ,
(10.0, 43.0, {'weight': 1.0938913337235003}) ,
(11.0, 76.0, {'weight': 1.8066534138474315}) ,
(11.0, 22.0, {'weight': 1.5814274601380762}) ,
(12.0, 68.0, {'weight': 0.82964162447510292}) ,
(12.0, 28.0, {'weight': 0.56687613489965616}) ,
(13.0, 41.0, {'weight': 0.67883257822079479}) ,
(13.0, 70.0, {'weight': 0.69594526555853065}) ,
(13.0, 39.0, {'weight': 0.62690609201673064}) ,
(14.0, 42.0, {'weight': 0.51384098628821639}) ,
(15.0, 91.0, {'weight': 0.80363040334950342}) ,
(15.0, 63.0, {'weight': 0.74055429404201112}) ,
(16.0, 75.0, {'weight': 0.89225782872169068}) ,
(16.0, 36.0, {'weight': 0.97796463842832249}) ,
(16.0, 61.0, {'weight': 1.2426060084547763}) ,
(17.0, 24.0, {'weight': 0.48569989925661516}) ,
(17.0, 88.0, {'weight': 0.58411688395739225}) ,
(17.0, 42.0, {'weight': 0.48569989925661516}) ,
(18.0, 19.0, {'weight': 0.73750301595928458}) ,
(18.0, 87.0, {'weight': 0.62985157194068553}) ,
(19.0, 80.0, {'weight': 0.77740196142918039}) ,
(20.0, 53.0, {'weight': 1.5817584651620507}) ,
(21.0, 33.0, {'weight': 1.558483049272277}) ,
(21.0, 35.0, {'weight': 1.022218339608882}) ,
(22.0, 93.0, {'weight': 1.4628634684132413}) ,
(22.0, 101.0, {'weight': 7.494583622053641}) ,
(23.0, 97.0, {'weight': 0.86085201141197409}) ,
(23.0, 90.0, {'weight': 1.4629842172999594}) ,
(23.0, 65.0, {'weight': 0.94746570241498318}) ,
(24.0, 34.0, {'weight': 0.55323853417352553}) ,
(25.0, 104.0, {'weight': 4.9839694794161371}) ,
(26.0, 85.0, {'weight': 1.5024751933287497}) ,
(26.0, 46.0, {'weight': 1.2053565344116006}) ,
(27.0, 72.0, {'weight': 0.72860577250944303}) ,
(27.0, 92.0, {'weight': 0.74002007166874428}) ,
(28.0, 54.0, {'weight': 0.55323853417352553}) ,
(29.0, 50.0, {'weight': 0.81426784351619774}) ,
(30.0, 98.0, {'weight': 0.77235026806254947}) ,
(30.0, 78.0, {'weight': 0.79413937142096647}) ,
(30.0, 95.0, {'weight': 0.78901093530213129}) ,
(31.0, 68.0, {'weight': 0.98851671776185412}) ,
(32.0, 95.0, {'weight': 0.8579399666494596}) ,
(34.0, 54.0, {'weight': 0.55323853417352553}) ,
(34.0, 55.0, {'weight': 0.60906522381767525}) ,
(35.0, 62.0, {'weight': 0.66697239833732958}) ,
(36.0, 93.0, {'weight': 1.2932994772208264}) ,
(37.0, 80.0, {'weight': 0.85527462610640648}) ,
(37.0, 96.0, {'weight': 0.85527462610640648}) ,
(38.0, 46.0, {'weight': 0.95334944284759993}) ,
(39.0, 50.0, {'weight': 0.52028039541706872}) ,
(40.0, 69.0, {'weight': 1.7931323073700682}) ,
(42.0, 62.0, {'weight': 0.51384098628821639}) ,
(42.0, 81.0, {'weight': 0.5466147583189902}) ,
(43.0, 65.0, {'weight': 1.0581157274507453}) ,
(44.0, 108.0, {'weight': 3.0598509599260266}) ,
(44.0, 70.0, {'weight': 1.0805691635112824}) ,
(45.0, 56.0, {'weight': 1.3420236519319457}) ,
(45.0, 79.0, {'weight': 1.6201017824952586}) ,
(46.0, 53.0, {'weight': 1.070516213146298}) ,
(47.0, 78.0, {'weight': 1.2822937333699174}) ,
(47.0, 103.0, {'weight': 3.9053251231648707}) ,
(48.0, 97.0, {'weight': 0.86085201141197409}) ,
(48.0, 67.0, {'weight': 0.75656062694199944}) ,
(49.0, 94.0, {'weight': 1.6216528905308547}) ,
(49.0, 86.0, {'weight': 0.80157999082131093}) ,
(49.0, 62.0, {'weight': 0.7081136236724922}) ,
(51.0, 102.0, {'weight': 1.4704389417937378}) ,
(51.0, 71.0, {'weight': 0.83506431983724716}) ,
(54.0, 75.0, {'weight': 0.70074754481170742}) ,
(55.0, 58.0, {'weight': 0.78571631647476448}) ,
(56.0, 82.0, {'weight': 1.3387438494166808}) ,
(57.0, 84.0, {'weight': 1.558483049272277}) ,
(59.0, 64.0, {'weight': 1.0416266944398496}) ,
(60.0, 98.0, {'weight': 1.2534403896544031}) ,
(63.0, 73.0, {'weight': 0.83646303763566465}) ,
(64.0, 72.0, {'weight': 0.8620326535711742}) ,
(66.0, 77.0, {'weight': 0.79981721989351606}) ,
(67.0, 72.0, {'weight': 0.74002007166874428}) ,
(69.0, 83.0, {'weight': 1.5000235782351021}) ,
(70.0, 77.0, {'weight': 0.75999034076724692}) ,
(71.0, 88.0, {'weight': 0.66450874893016454}) ,
(74.0, 97.0, {'weight': 0.8743417572549379}) ,
(76.0, 107.0, {'weight': 2.0300278349030831}) ,
(77.0, 89.0, {'weight': 0.75999034076724692}) ,
(79.0, 106.0, {'weight': 4.5661761296968333}) ,
(82.0, 95.0, {'weight': 1.083633962514291}) ,
(84.0, 99.0, {'weight': 2.1024875417678257}) ,
(89.0, 92.0, {'weight': 0.75419548272456249}) ,
(100.0, 107.0, {'weight': 2.9259491743365307}) ,
(101.0, 109.0, {'weight': 7.6747981730730297}) ,
(102.0, 108.0, {'weight': 4.3128725576385092}) ,
(104.0, 105.0, {'weight': 7.5515191839631273})]
G2 = nx.Graph()
G2.add_nodes_from(nodes)
G2.add_edges_from(edges)
G2.add_node('special', {'label': 'special'})
special_edges = []
for n, ndat in G2.nodes_iter(data=True):
if ndat['label']!='special' and ndat['label']>=0:
special_edges.append( (n,'special', {'weight':0}) )
G2.add_edges_from(special_edges)
for n, ndat in G2.nodes_iter(data=True):
if ndat['label']==-1:
path = nx.shortest_path(G2, source=n, target='special', weight='weight')
ndat['closest'] = path[-2] #Closest node with label>=0
G2.remove_node('special')
Upvotes: 2
bigballer
Reputation: 146
h = heapq
solution = {}
g = build_nx_graph()
for node in g:
if label_is_neg_1(node):
solution[node] = false
heappush(h, (0, node))
while h:
distance, node = heappop(h)
for neighbour, neighbour_dist in iterate_neighbours(g):
bs = best_solution(neighbour, neighbour_dist)
if not bs == solution.get(neighbour, bs):
solution[neighbour] = bs
heappush(h, (bs, neighbour))
if len(solution) == len(g):
break
this incomplete pseudocode should start at all the -1 nodes, and "fan out", calculating the distance to all the non -1 nodes in order.
Upvotes: 0
Ilovescience
Reputation: 133
If I understand your problem then you have a travelling salesman problem, which means there is no exact solution faster than (in the worst case) testing ever single possibility.
Upvotes: 0
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