Finding Shortest path in weighted directional multigraph with extra constraints

Question

Given a weighted directed multigraph, I have to find shortest path between starting vertex u to vertex v. Apart from weight, each edge also has time. The path connecting u and v cannot take more than a given maximum time. The trouble is while using Djikstra, there are chances that shortest path takes more time than the limit.

My approach is to find all valid paths between u and v and than minimize the weight. But the approach is not practical due to its high complexity.

Any ideas?

Answer 1

如果体重足够小

在这种情况下，您可以为每个节点执行的操作，存储您可以在该节点的路径上获得的所有可能的权重总和。现在你可以在这个新图上做dijsktra，并尝试最小化成对节点（node，weight_sum）的时间。

如果时间足够小

您可以执行与上一示例相同的操作，但可以使用对（节点，时间）。

一般问题

我担心，一般来说，你所能做的就是尝试所有可能的路径，尝试用撬开来改善它。