日元的K最短路径给出错误的结果（Python）

Question

我正在尝试基于https://en.wikipedia.org/wiki/Yen%27s_algorithm的伪代码来实现日元K最短路径算法。这是代码。

import numpy as np
import networkx as nx

edge_list = [[0, 1], [0, 2], [0, 7], [1, 2], [1, 9], [2, 5], [2, 7], [2, 9], [3, 4], [3, 5], [3, 6], [3, 8], [4, 5], [4, 6], [4, 7], [4, 8], [5, 6], [5, 7], [5, 8], [6, 8], [7, 8]]
graph = nx.Graph()
graph.add_edges_from(edge_list)
nx.draw(graph, with_labels = True)
source_node = 8
destination_node = 9

def yen_ksp(graph, source, sink, K):
    A, B = [], []
    A.append(nx.shortest_path(graph, source=source, target=sink))
    for k in range(1, 1+K):
        for i in range(len(A[k - 1]) - 1):
            spurNode = A[k-1][i]
            rootPath = A[k-1][0:i+1]
            removed_edges, removed_nodes = [], []
            for p in A:
                if rootPath == p[0:i+1] and p[i:i+2] not in removed_edges:
                    removed_edges.append(p[i:i+2])

            for edge in removed_edges:
                graph.remove_edge(edge[0], edge[1])
            try:
                spurPath = nx.shortest_path(graph, source=spurNode, target=sink)
            except:
                for edge in removed_edges:
                    graph.add_edge(edge[0], edge[1])
                continue

            totalPath = rootPath + spurPath[1:]
            B.append(totalPath)
            for edge in removed_edges:
                graph.add_edge(edge[0], edge[1])

        if B == []:
# This handles the case of there being no spur paths, or no spur paths left.
# This could happen if the spur paths have already been exhausted (added to A), 
# or there are no spur paths at all - such as when both the source and sink vertices 
# lie along a "dead end".
           break
        B.sort()
        A.append(B[-1])
        B.pop(-1)
    return A

print(yen_ksp(graph.copy(), source_node, destination_node, 10))

这应该是根据上述代码生成的无向，无权图。

这是代码的输出。

[[8, 5, 2, 9],
 [8, 7, 2, 9],
 [8, 7, 2, 1, 9],
 [8, 7, 2, 1, 2, 9],
 [8, 7, 2, 1, 2, 1, 9],
 [8, 7, 2, 1, 2, 1, 2, 9],
 [8, 7, 2, 1, 2, 1, 2, 1, 9],
 [8, 7, 2, 1, 2, 1, 2, 1, 2, 9],
 [8, 7, 2, 1, 2, 1, 2, 1, 2, 1, 9],
 [8, 7, 2, 1, 2, 1, 2, 1, 2, 1, 2, 9],
 [8, 7, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 9]]

显然，该算法缺少较短的路径。并且，结果包含具有循环的路径。我只想要那些没有的。

此外，在其他情况下，结果顺序错误，一些较长的路径出现在其他较短的路径之前。在KSP问题中，结果的顺序显然很重要，因为如果我停在某个k点，我想确保没有我错过的更短路径。

我愿意接受其他算法，这些算法可以正确有效地解决KSP的这一问题，并且在无向非加权图上没有循环。

请帮助。

Answer 1

Networkx提供了从最短路径开始生成从源到目标的图形中所有简单路径的列表的功能：shortest_simple_paths。该过程完全基于Yen的算法，您可以在文档中阅读。

使用非常简单：

shortest_simple_paths

如果只需要前K条最短路径，则可以使用paths = list(nx.shortest_simple_paths(graph, source_node, target_node)) ：

islice

示例：

islice

输出：

from itertools import islice
paths = list(islice(nx.shortest_simple_paths(graph, source_node, target_node), K))

如果您想了解

from itertools import islice

K = 10
source_node = 8
target_node = 9

graph = nx.Graph()
edge_list = [[0, 1], [0, 2], [0, 7], [1, 2], [1, 9], [2, 5], [2, 7],
             [2, 9], [3, 4], [3, 5], [3, 6], [3, 8], [4, 5], [4, 6],
             [4, 7], [4, 8], [5, 6], [5, 7], [5, 8], [6, 8], [7, 8]]
graph.add_edges_from(edge_list)

for path in islice(nx.shortest_simple_paths(graph, source_node, target_node), K):
    print(path)

的实现方式，可以查看其

[8, 5, 2, 9]
[8, 7, 2, 9]
[8, 5, 7, 2, 9]
[8, 5, 2, 1, 9]
[8, 3, 5, 2, 9]
[8, 7, 0, 1, 9]
[8, 7, 2, 1, 9]
[8, 4, 5, 2, 9]
[8, 7, 5, 2, 9]
[8, 7, 0, 2, 9]

：它写得很好并且很容易理解！