graph serialization

I'm looking for a simple algorithm to 'serialize' a directed graph. In particular I've got a set of files with interdependencies on their execution order, and I want to find the correct order at compile time. I know it must be a fairly common thing to do - compilers do it all the time - but my google-fu has been weak today. What's the 'go-to' algorithm for this?

From stackoverflow Kieron

• I would expect tools that need this simply walk the tree in a depth-first manner and when they hit a leaf, just process it (e.g. compile) and remove it from the graph (or mark it as processed, and treat nodes with all leaves processed as leaves).

  As long as it's a DAG, this simple stack-based walk should be trivial.

  sleske : Yes, that's how you do it. It's called a depth-first search (DFS). And unless you are certain you have a DAG, you mustcheck for back edges, otherwise a cycle will send you into an infinite loop.
  From Kevin Ballard

• I've come up with a fairly naive recursive algorithm (pseudocode):

  Map<Object, List<Object>> source; // map of each object to its dependency list
  List<Object> dest; // destination list
  
  function resolve(a):
      if (dest.contains(a)) return;
      foreach (b in source[a]):
          resolve(b);
      dest.add(a);
  
  foreach (a in source):
      resolve(a);
  

  The biggest problem with this is that it has no ability to detect cyclic dependencies - it can go into infinite recursion (ie stack overflow ;-p). The only way around that that I can see would be to flip the recursive algorithm into an interative one with a manual stack, and manually check the stack for repeated elements.

  Anyone have something better?

  From Kieron

• Topological Sort. From Wikipedia:

  In graph theory, a topological sort or topological ordering of a directed acyclic graph (DAG) is a linear ordering of its nodes in which each node comes before all nodes to which it has outbound edges. Every DAG has one or more topological sorts.

  Pseudo code:

  L ← Empty list where we put the sorted elements
  Q ← Set of all nodes with no incoming edges
  while Q is non-empty do
      remove a node n from Q
      insert n into L
      for each node m with an edge e from n to m do
          remove edge e from the graph
          if m has no other incoming edges then
              insert m into Q
  if graph has edges then
      output error message (graph has a cycle)
  else 
      output message (proposed topologically sorted order: L)
  

  Benjol : Eh... copied directly off wikipedia?

  Jason S : yes, please cite sources
  From Andrew Peters

• If the graph contains cycles, how can there exist allowed execution orders for your files? It seems to me that if the graph contains cycles, then you have no solution, and this is reported correctly by the above algorithm.

  sleske : Yes, a topological sort is not possible if a graph contains cycles. This corresponds to the real world: If I ask you to do A before B, *and* B before A, there's no way you're gonna satisfy me ;-).
  From $pageUsers[$post.author].name