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Graph serialization

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?

Asked by: Guest | Views: 55
Total answers/comments: 4
Guest [Entry]

"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)
output message (proposed topologically sorted order: L)"
Guest [Entry]

"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."
Guest [Entry]

"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."
Guest [Entry]

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