How do I find all paths through a set of given nodes in a DAG?

Question

I have a list of items (blue nodes below) which are categorized by the users of my application. The categories themselves can be grouped and categorized themselves.

The

Answer 1

Despite the fact that your graph is acyclic, the operations you cite remind me of similar aspects of control flow graph analysis. There is a rich set of algorithms based on dominance that may be applicable. For example, your third operation reminds me od computing dominance frontiers; I believe that algorithm would work directly if you temporarily introduce "entry" and "exit" nodes. The entry node connects the "given set of nodes" and the exit nodes connects the sinks.

Also see Robert Tarjan's basic algorithms.