Let’s say I have a directed graph represented as an adjacency matrix, and I’m given two nodes $ u,v$ and a parameter $ k$ . Let’s also say that the maximal degree of a node in the graph is $ d$ .
What is the most efficient algorithm to find all paths of length $ <=k$ from $ u$ to $ v$ ?
I know the number of such paths can be calculated efficiently using Dynamic Programming approach, but I’m looking for an algorithm that allows to get a set of actual paths.
It’s clear that such algorithm would have a factor of the number of paths in its time complexity, which has $ k$ in the exponent, but still, I would like to know what is the best approach for such a problem.