Topological Sorts

A graph is a partial order which is weaker than <.
A topological sort converts a partial order into a full ordering.
There can be many topological sorts for a given graph (or none may be possible).
There exists a topological sort for all DAGs.
For disconnetced graphs, there are always multple topo-sorts.

There are two algorithms for topo-sorting.

1) Do a breadth first search.  As each node is finished, place it at the front of the list.
2) Find a node with in-degree of zero.  Put it in the back of the list.  Remove the node fom the graph.  Repeat.

Uses:

• Task Management
• Clothes
• Subexpressions and code fragements
  
• Computing cells in a sreadsheet
• Sports Ranking

   
Links:
http://www.cs.auckland.ac.nz/~ute/220ft/graphalg/node16.html