Graph algorithms - DFS, generators callbacks, and optimisation

Discussion in 'Python' started by Paul Moore, Nov 29, 2003.

  1. Paul Moore

    Paul Moore Guest

    I'm trying to check a graph (represented in the usual Python adjacency
    list format) for loops. This is dead simple - you use a depth-first
    search, and look out for "back edges" (edges from a vertex "back" to
    one you've already seen).

    I already have a DFS algorithm which generates each edge in turn. It's
    great for what it does, but it ignores back edges.

    def DFS(graph, start, seen = None):
    if not seen:
    seen = {start: 1}
    for v in graph[start]:
    if v not in seen:
    seen[v] = 1
    yield start, v
    if v in graph:
    for e in DFS(graph, v, seen):
    yield e

    I could code a variation on this, just for this one problem, but that
    sort of cut and paste coding offends me (and DFS is *just* fiddly
    enough that I'm not confident of getting it right each time I
    reimplement it). So what I'd rather do is enhance my existing code to
    be a bit more general.

    I have a C++ reference which implements a highly general DFS
    algorithm, using the visitor pattern (pass a visitor object to the
    function, and various callback methods are called at points in the
    algorithm - there are discover_vertex, discover_edge, back_edge, etc

    I could code something like this (the pseudocode for the algorithm is
    almost executable in Python!) but it doesn't feel particularly
    "pythonic". Having to write a visitor class for each use case feels
    unwieldy (as well as being perceptibly slower than the generator
    implementation). Having the various callbacks as arguments (pass a
    callable or None) isn't much faster or cleaner.

    Can anybody think of a good way of making the DFS code above a little
    more generic, without losing the efficient and simple (from the
    caller's POV) approach of the current version?

    Paul Moore, Nov 29, 2003
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  2. Paul Moore

    Robin Becker Guest

    Well in this case couldn't you make seen do the detection for you.
    If I understand your analysis you could make the seen dictionary a
    special kind of dictionary.


    class DFSSeen(dict):
    def __contains__(self,x):
    r = super(DFSSeen,self).__contains__(x)
    if r:
    print 'back link to',x
    return r

    G = {
    1: (2,3),
    2: (3,5),
    3: (4,),
    4: (6,),
    5: (2,6),
    6: (1,),
    for v in DFS(G,1,DFSSeen({1:1})):
    print v

    using the above I get
    (1, 2)
    (2, 3)
    (3, 4)
    (4, 6)
    back link to 1
    (2, 5)
    back link to 2
    back link to 6
    back link to 3

    so cycle detection is possible without altering the original code, but
    it probably isn't sufficient for your purposes in that we don't have the
    start vertex.


    Robin Becker, Nov 29, 2003
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  3. Paul Moore

    Paul Moore Guest

    Interesting trick. I hadn't thought of this, mainly because "seen" is
    only in the parameter list to allow the recursive call to work - I'd
    never intended it to be passed by the user. (I have a non-recursive
    version of DFS without a "seen" parameter).

    More general DFS algorithms have a "colour" dictionary, where vertices
    can be "White" (not seen) "Black" (seen) or "Grey" (essentially,
    "still being looked at"). I'm not sure how that would interact with
    this trick.

    Hmm. I wish I had a "big" use case where issues like this matter. But
    all of my uses are small - the sort of thing where a general library
    helps a lot, because the whole project is too small to justify
    (re-)implementing the algorithm. But with just small examples, you
    never get the breadth of use cases to make the optimal design obvious.

    Or maybe I'm just a lousy library designer :)

    Time to stop rambling and do something productive...

    Paul Moore, Nov 29, 2003
  4. Not very tested, but how about (borrowing Robin's example data):

    ====< >=============================================
    def DFS2(graph, start, rlevel=0, seen = None):
    if seen is None: seen = {}
    seen[start] = 1 # allow for jumping into arbitrary subtrees with
    # same seen dict in new generator ?
    for v in graph[start]:
    is_back = v in seen
    seen[v] = True # ok if redundant
    yield (start, v), is_back, rlevel
    if not is_back:
    if v in graph:
    for e in DFS2(graph, v, rlevel+1, seen):
    yield e

    if __name__ == '__main__':
    G = {
    1: (2,3),
    2: (3,5),
    3: (4,),
    4: (6,),
    5: (2,6),
    6: (1,),
    for e, is_back, level in DFS2(G, 1):
    print '%s%s -> %s%s' %(level*' ',e[0], e[1], ('',' (back)')[is_back])

    The output is:

    [15:15] C:\pywk\clp>
    1 -> 2
    2 -> 3
    3 -> 4
    4 -> 6
    6 -> 1 (back)
    2 -> 5
    5 -> 2 (back)
    5 -> 6 (back)
    1 -> 3 (back)
    My .02 above ;-)

    Bengt Richter
    Bengt Richter, Nov 29, 2003
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