Python 查找到具有属性的多个节点之一的最短路径

我有一个networkx图，表示大约100万个对象（顶点）的最小生成树。我想知道是否有一种有效的方法可以找到给定顶点和许多其他顶点之间的最短路径

下面是一个顶点数较少的示例图（110）

我想要的是“标签>=0的哪个顶点最接近标签为-1的每个顶点”。对于这样一个小图，蛮力方法使用类似于

nx.all_pairs\u dijkstra\u path\u length（）

的东西，然后检查标签，效果很好，但它不能扩展到非常大的图。是否有更有效的算法，特别是如果内置到networkx，我可以使用

更新：

我用Richard的建议和下面的评论写了这篇文章。我真正想要的是一系列的标签，我认为这让事情不像Richard在networkx中提到的那样混乱。整个重新标记在一个数据集上花费了45秒，而暴力只花了一个小时

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

---

我不认为networkx中内置了这样的算法，但似乎有一种算法可以扩展成本最低的路径，直到达到某个条件为止。然而，即使networkx不包含这样的功能，构建一个算法来实现这一点也非常容易

• 使用

  label==-1

  调用源节点
• 将距离源节点最近的

  label>=0

  节点称为目标节点。我们的目标是找到目标节点
• 创建一个新节点。这将是特殊节点
• 将所有潜在目标节点连接到具有权重为0的边的特殊节点
• 对于每个源节点，查找到特殊节点的最短路径。此路径上的倒数第二个节点必须是目标节点，并且是距离源节点最近的节点
• 完成后，删除特殊节点及其所有连接边

如果源节点数为S，则该算法以O（S（| E |+| V | log | V |）时间运行（假设最短路径算法为Dijkstra）

（可能是我误解了您是希望-1最接近>=0还是>=0最接近-1。如果我有，只需反转源/目标标签。）

---

如果我理解你的问题，那么你有一个旅行推销员的问题，这意味着没有确切的解决方案比（在最坏的情况下）测试任何单一的可能性更快

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

---

这个不完整的伪代码应该从所有的-1节点开始，然后“扇出”，依次计算到所有非-1节点的距离。

这里有任何边长度吗？或者它们是统一的吗？你不是在一个Dijkstra调用中通过从特殊节点搜索到源节点来实现这一点吗？是的，尽管这只适用于无向图。我在写这篇文章的时候考虑过你的想法，我认为如果你正在构建自己的算法，这是最直接的路线。但是，使用networkx框架实现它要比我这里介绍的复杂得多。您可以在每次运行最短路径算法后，通过最短路径中的节点，跟踪与特定节点的距离，并从图形中删除最短路径节点，从而加快此算法的速度。每次删除节点时，将其相邻节点连接到具有适当计算距离的特殊节点。（每个被删除的节点，如果是-1节点，也记录下它的解决方案）。@robertking:这可能有效，但简单是一种美德。如果您查看OP对他们问题的编辑，他们的运行时间从1小时减少到45秒。进一步算法开发的潜在节省可能会被此时的开发时间大大抵消。如果代码被频繁使用的话，也许值得一试。

#!/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')

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