在具有正权重的有向图中找到最短循环
[英]Find the shortest cycle in a directed graph with positive weights
问题描述
A similar question of mine was asked in the below link, where one of the comments states that "The problem is certainly NP-hard because TSP can be reduced to it".
在下面的链接中提出了我的一个类似问题，其中一条评论指出“这个问题肯定是 NP 难的，因为 TSP 可以减少到它”。
Finding shortest circuit in a graph that visits X nodes at least once 在至少访问 X 节点一次的图中查找最短路
On the other hand, in another link shown below, one of the solutions says that by modifying Dijkstra's algorithm, the complexity would be $O(n^3)$.另一方面，在下面显示的另一个链接中，其中一个解决方案表示通过修改 Dijkstra 算法，复杂度将为 $O(n^3)$。
Find cycle of shortest length in a directed graph with positive weights 在具有正权重的有向图中找到最短长度的循环
I am wondering which solution in one of those links is correct.我想知道其中一个链接中的哪个解决方案是正确的。
1 个解决方案
解决方案1
1 2023-01-04 13:45:17
From your description you only want to find any shortest cycle, so the second link applies to you and you can find an efficient algorithm.根据您的描述，您只想找到最短的周期，因此第二个链接适用于您，您可以找到一种有效的算法。 In the first case the question asked for the shortest cycle going through some set of vertices.在第一种情况下，问题要求通过某些顶点集的最短周期。
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