Question

I’m curious if there is a specific graph algorithm that traverses an unweighted acyclic directed graph by choosing a start node and then proceeding via DFS. If a node is encountered that has unsearched predecessors then it should back track the incoming paths until all paths to start have been explored.

I found a wikipedia category for graph algorithms but there is a small sea of algorithms here and I’m not familiar with most of them.

EDIT: example:
given the graph {AB, EB, BC, BD}, traverse as: {A,B,E,B,C,D} or unique order as {A,B,E,C,D}.
Note this algorithm unlike BFS or DFS does not need to begin again at a new start node if all paths of the first start node are exhausted.

Answer 1

In DFS, you usually choose the vertex to be visited after u based on the edges starting at u. You want to choose based first on the edges ending at u. To do this, you could have a transpose graph info, and try to get the vertex from there first.

It would be something like this:

procedure dfs(vertex u)
  mark u as visited
  for each edge (v, u) //found in transpose graph
    if v not visited
      dfs(v)
  for each edge (u, w)
    if v not visited
      dfs(w)