Question

I have recently discovered graphs and algorithms and am trying to solve a specific problem involving two different types of vertices: Users and Entities. Details are as follows:

• The graph is directed
• I am trying to find all paths from A to B
• A is always a User
• B can be a User or an Entity
• If B is a User, maximum depth for the search is 3 edges
• If B is an Entity, maximum depth is 2 edges
• I can not traverse any edges which are outbound from a User, unless the user is A

Although the graph has two types of vertices, it is not bipartite.

So far I have managed to create a graph object which holds a vertex-indexed array of adjacency lists. The adjacency lists are based on linked lists.

I think I require some kind of variation on an All Paths algorithm, but I’m not quite sure. In addition, not sure whether I should be looking at DFS or BFS.

I am working in PHP, which complicates matters, since most examples are in Java. What I’d really like is the pseudo code.

Any ideas? Thanks!

Answer 1

It sounds like you’re traversing some sort of LDAP implementation. If you need a generic algorithm, just use a DFS, since it’s easier to code. Doing this is overkill though unless the depth will change.

Most generic way

 dfs(A,B):
     return dfs(A,B,1);

 dfs_(u,B,depth):
     if u == B:
          return u;

     if (u is User and depth > 3) or (u is Group and depth > 2):
          return None;       

     out = [];
     for children of thing:
          return max( dfs_(children,depth+1) ) # take the non-null one
     out.append(u);
     return out;