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Finding cycles in a graph

  1. Feb 15, 2016 #1
    1. The problem statement, all variables and given/known data
    Capture.PNG

    2. Relevant equations
    Recursion, graphs, DFS
    3. The attempt at a solution
    To try to solve this algorithm, I first need to find all the basic cycles in the Graph G. When I have these cycles, I can simply pick the smallest edge in each of them and add them to the set F, while removing duplicates, which is trivial. However, I can't figure out an algorithm that would give me all the cycles in polynomial time.

    I tried using a modified Depth First Search recursive method that, when it reaches a node that has already been visited, backtracks until it reaches again to find the cycle. However, for a simple graph with 8 nodes and 14 links my method gets called more than 500 times... I tried using what is described here: http://stackoverflow.com/questions/546655/finding-all-cycles-in-graph/549312#549312

    Am I thinking about this problem correctly? What approach other than finding the cycles could I use? Thanks
     
  2. jcsd
  3. Feb 15, 2016 #2
    Could I simply use Boruvka's algorithm to get a minimum spanning tree and add these edges to F?
     
  4. Feb 16, 2016 #3
    I think all the edges that are not in a maximum spanning tree wil give me the minimum hitting set.
     
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