使用时间约束查找图形中的所有可能路径

Question

我的数据如下所示：

$rest = "";
$re = '~\b(https?://)www\.myweb\.com/(\S+\b)~'; 
$str = "Some text https://www.myweb.com/page/cat/323123442321-rghe432, another http://www.myweb.com/page/cat/323123442321-rghe432 and then another https://www.adifferentsite.com/fsdhjss/erwr"; 
echo $result = preg_replace_callback($re, function ($m) use (&$rest) {
    $rest = $m[2];
    return $m[1] . "embed.myweb.com/" . $m[2];
}, $str, 1) . PHP_EOL;
//-LIMIT ^ - HERE -
echo $rest;

• source target time 0.5 96253 94861 1.0 96652 95091 1.5 94861 95091 2.5 95091 95409 3.5 95409 97221 4.5 97221 96781 5.5 96781 97707 6.5 97707 98191 7.5 98191 99096 8.5 99096 100016 8.5 99096 100013 9.5 100013 98663 9.5 100016 98658 10.5 98658 99573 10.5 98663 99589 11.5 99589 100506 11.5 99573 100490 和source列中的每个整数都会引用一个点。
• 每一行都是两个点之间的链接。
• target索引是指可以找到链接的时间点。

智能算法将找到数据集中包含的所有可能轨迹。

例如，在前面的示例中，存在4个轨迹：

time

这个问题可以恢复为图论问题。请参见下图，该图对应于开头显示的数据。

这个想法是在这个图中找到所有可能的路径 一个关于时间逻辑的约束：一个轨迹是一个有序的点（节点）列表，它只能来自[96253, 94861, 95091, 95409, 97221, 97221, 96781, 97707, 98191, 99096, 100016, 98658, 99573, 100490] [96652, 95091, 95409, 97221, 97221, 96781, 97707, 98191, 99096, 100016, 98658, 99573, 100490] [96253, 94861, 95091, 95409, 97221, 97221, 96781, 97707, 98191, 99096, 100013, 98663, 99589, 100506] [96652, 95091, 95409, 97221, 97221, 96781, 97707, 98191, 99096, 100013, 98663, 99589, 100506] 到t（不能过去）。

该算法将在Python中实现。所以允许任何Python技巧： - ）

Answer 1

应用图论算法似乎是解决这个问题的明智方法。我使用了networkx python库。

print(spot_ids)

输出：

      source  target
time                
0.5    96253   94861
1.0    96652   95091
1.5    94861   95091
2.5    95091   95409
3.5    95409   97221
4.5    97221   96781
5.5    96781   97707
6.5    97707   98191
7.5    98191   99096
8.5    99096  100016
8.5    99096  100013
9.5   100013   98663
9.5   100016   98658
10.5   98658   99573
10.5   98663   99589
11.5   99589  100506
11.5   99573  100490

算法：

import itertools
import networkx as nx

# Build graph
graph = nx.Graph()
for t, spot in spot_ids.iterrows():
    graph.add_edge(int(spot['source']), int(spot['target']), attr_dict=dict(t=t))

# Find graph extremities by checking if number of neighbors is equal to 1
tracks_extremities = [node for node in graph.nodes() if len(graph.neighbors(node)) == 1]
tracks_extremities

paths = []
# Find all possible paths between extremities
for source, target in itertools.combinations(tracks_extremities, 2):

    # Find all path between two nodes
    for path in nx.all_simple_paths(graph, source=source, target=target):

        # Now we need to check wether this path respect the time logic contraint
        # edges can only go in one direction of the time

        # Build times vector according to path
        t = []
        for i, node_srce in enumerate(path[:-1]):
            node_trgt = path[i+1]
            t.append(graph.edge[node_srce][node_trgt]['t'])

        # Will be equal to 1 if going to one time direction
        if len(np.unique(np.sign(np.diff(t)))) == 1:
            paths.append(path)

for path in paths:
    print(path)

输出：

[100490, 99573, 98658, 100016, 99096, 98191, 97707, 96781, 97221, 95409, 95091, 96652]
[100490, 99573, 98658, 100016, 99096, 98191, 97707, 96781, 97221, 95409, 95091, 94861, 96253]
[96652, 95091, 95409, 97221, 96781, 97707, 98191, 99096, 100013, 98663, 99589, 100506]
[100506, 99589, 98663, 100013, 99096, 98191, 97707, 96781, 97221, 95409, 95091, 94861, 96253]