Research algorithms to optimize the placements

1. Find the longest cycle in the graph

• Depth First Search (DFS) (applying to find the cycle)
• Finding cycles in a directed graph (newsgroup and mailing list archives in the net)
• How to detect circle in a directed graph
• Finding all cycles in graph
• Best algorithm for detecting cycles in a directed graph
• Detecting cycles in directed graph
• Good way to find ALL cycles within a graph
• Strongly connected components
• Tarjan's strongly connected components algorithm
• Cycle detection
• Strongly connected components (Lecture notes)
  

2. Find all pairs shortest path Algorithm

* Sample Code: http://www.codeguru.com/cpp/cpp/algorithms/article.php/c5119
* Shortest Path Algorithms: http://www.umich.edu/~me558/manuals/LEDA/shortest_path.html

3. Detect a cycle in the graph

* Extending the shortest-path swarm algorithm to cycle detection: http://ieeexplore.ieee.org/Xplore/login.jsp?url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F10622%2F33557%2F01594255.pdf%3Farnumber%3D1594255&authDecision=-203