Seeking algorithm to invert (reverse? mirror? turn inside-out) a DAG

Question

I\'m looking for an algorithm to \"invert\" (reverse? turn inside-out?) a DAG:

       A*      # I can\'t ascii-art the arrows, so just
      / \\      # pretend          


        

Answer 1

I solved this with a simple graph traversal. Keep in mind topological sorting will only be useful for directed acyclic graphs.

I used an adjacency list, but you can do a similar thing with an adjacency matrix.

In Python it looks like this:

# Basic Graph Structure
g = {}
g[vertex] = [v1, v2, v3] # Each vertex contains a lists of its edges

To find all the edges for v, you then traverse the list g[v] and that will give you all (v, u) edges.

To build the reversed graph make a new dictionary and build it something like this:

    reversed = {}
    for v in g:
        for e in g[v]:
            if e not in reversed:
                reversed[e] = []
            reversed[e].append(v)

This is very memory intensive for large graphs (doubling your memory usage), but it is a very easy way to work with them and quite quick. There may be more clever solutions out there involving building a generator and using a dfs algorithm of some sort, but I have not put a lot of thought into it.