生成树的顶点大约为100万个。我想知道是否有一种有效的方法来找到一个给定顶点和许多其他顶点之间的最短路径。在
下面是一个顶点数较少的示例图(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)
我想要的是“哪个顶点的label>;=0最接近label=-1的每个顶点”。对于这样的小图,使用nx.all_pairs_dijkstra_path_length()
之类的方法,然后检查标签的brute-force方法可以很好地工作,但是不能扩展到非常大的图。有没有更有效的算法,特别是如果内置到networkx中,我可以使用吗?在
更新:
我用理查德的好建议和下面的评论来写这篇文章。我真正想要的是一系列的标签,我认为这使得事情不像Richard在networkx中提到的那样混乱。在一个数据集上,整个重新标记花费了45秒,用了一个小时的暴力!在
^{pr2}$
这个不完整的伪代码应该从所有-1节点开始,然后“扇出”,依次计算到所有非1节点的距离。在
我不认为networkx中有这样的算法,但似乎有一个算法可以扩展最小成本路径,直到达到某个条件。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还是相当容易的。在
label==-1
调用节点作为源节点。在label>=0
的节点称为其目标节点。我们的目标是找到目标节点。在如果源节点数为S,则该算法在O(S(| E |+| V |))时间内运行(假设最短路径算法为Dijkstra)。在
(可能是我误解了您是希望-1最接近>;=0,还是>;=0最接近-1。如果有,请颠倒源/目标标签。)
如果我理解你的问题,那么你就有了一个旅行推销员的问题,这意味着没有比(在最坏的情况下)测试任何单一可能性更快的精确解决方案。在
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