查找两个图节点之间的所有路径 [英] Find all paths between two graph nodes

问题描述

我正在研究 Dijkstras 算法的实现，以检索路由网络上互连节点之间的最短路径.我有实施工作.当我将起始节点传递给算法时，它返回所有节点的所有最短路径.

I am working on an implemtation of Dijkstras Algorithm to retrieve the shortest path between interconnected nodes on a network of routes. I have the implentation working. It returns all the shortest paths to all the nodes when I pass the start node into the algorithm.

我的问题:如何检索从节点 A 到节点 G 的所有可能路径，甚至从节点 A 返回到节点 A 的所有可能路径

My Question: How does one go about retrieving all possible paths from Node A to say Node G or even all possible paths from Node A and back to Node A

推荐答案

寻找所有可能的路径是一个难题，因为简单路径的数量是指数级的.即使找到第 k 个最短路径 [或最长路径] 也是 NP-Hard.

Finding all possible paths is a hard problem, since there are exponential number of simple paths. Even finding the kth shortest path [or longest path] are NP-Hard.

找到从 s 到 t 的所有路径 [或所有路径达到特定长度的所有路径] 的一种可能解决方案是 BFS，不保留 visited 集，或者对于加权版本 - 您可能想要使用 统一成本搜索

One possible solution to find all paths [or all paths up to a certain length] from s to t is BFS, without keeping a visited set, or for the weighted version - you might want to use uniform cost search

请注意，在每个具有循环的图中 [它不是 DAG]是 s 到 t 之间的无限路径.

Note that also in every graph which has cycles [it is not a DAG] there might be infinite number of paths between s to t.

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