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Re^10: Finding All Paths From a Graph From a Given Source and End Node

by LanX (Cardinal)
on Nov 02, 2010 at 15:56 UTC ( #869033=note: print w/replies, xml ) Need Help??


in reply to Re^9: Finding All Paths From a Graph From a Given Source and End Node
in thread Finding All Paths From a Graph From a Given Source and End Node

It did.! Just counting, it took 12% longer than mine which invokes a callback for each path.

interesting ... I'll take a look at it tomorrow!

Cheers Rolf

UPDATE: I expected this part { %$seen } to be quite expensive .... does it even make sense?

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Re^11: Finding All Paths From a Graph From a Given Source and End Node
by BrowserUk (Pope) on Nov 02, 2010 at 17:09 UTC
    UPDATE: I expected this part { %$seen } to be quite expensive .... does it even make sense?

    Well, it does no harm :)

    Um. Do you mean:

    • Does the syntax make sense?

      It just makes a copy (anonymous reference) of the seen hash(ref).

    • Or; why make a copy?

      I make a copy because I want any changes made to it at deeper levels of recursion, to be unwound as the recursion unwinds.

      It's purpose is obviously to prevent the algorithm from going in circles when it re-encounters a node it has already visited. But when we visit a node a deeper level we don't to permanently prevent it from visiting that node again if it reaches it via different path earlier in the recursion but later in the iteration.

      Hm. Not sure that description works?

    Essentially, the hash(ref) $seen and array(ref) $path contain the same information, but arrays are no good for lookup, and hashes are unordered which is no good for paths. Hence using both.

    There is a potential optimisation there. I could just build the hash from the array at each level instead of passing it through. In fact, I'll try that later.


    Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
    "Science is about questioning the status quo. Questioning authority".
    In the absence of evidence, opinion is indistinguishable from prejudice.

      Hi,

      Even though this thread is about 6 months old I find it really very useful, as I am currently working on a similar project and have struggled with it, being quite a young programmer.I have read through it all and feel that I might be able to get the help that I need.

      I have a network containing about 2500 edges (directed) and I am looking at being able to work out all the routes downstream from a given beginning node. The difference from neversaint's problem is that both beginning and end nodes are supplied in his.My initial concerns was that it'd result in very large output that may not be manageable but considering that it is currently not a very large network and that I really need to identify all the routes i am willing to give it a try.

      I will be happy to have your inputs and thoughts

      Thank you very much in advance

        I have a network containing about 2500 edges (directed) and I am looking at being able to work out all the routes downstream from a given beginning node.

        Hm. What is your terminating condition?

        A directed graph can contain loops:

        a->b->c ^ | | v e<-d

        If your starting node is (a), when do you decide you've reach the (an) end?

        Every time around the b->c->d->e->b loop, could be seen as another route. The only logical basis I can see for breaking that impasse is a rule along the lines of "Stop when there is no possibility of reaching a so far unvisited node. And that could be quite difficult to program efficiently.

        As so often, more info required?


        Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
        "Science is about questioning the status quo. Questioning authority".
        In the absence of evidence, opinion is indistinguishable from prejudice.
Re^11: Finding All Paths From a Graph From a Given Source and End Node
by LanX (Cardinal) on Nov 02, 2010 at 18:58 UTC
    And the culprit was ... usage of self-documenting variable names.

    Simply avoiding the array-copy my @path=@_ makes a factor 4.5 performance boost...

    Fascinating!!! What a pity Perl doesn't support aliasing out of the box!

    { my %seen; sub track { my $last=$_[-1]; $seen{$last}=1; for my $next (@{$graph{$last}}) { next if $seen{$next}; if ($next eq $stop) { #print join ("->",@_,$stop),"\n"; $anzahl++; print "$anzahl at ",time-$time0,"\n" if $anzahl%10000==0; } else { track(@_,$next); } } delete $seen{$last}; } }

    Cheers Rolf

      Simply avoiding the array-copy my @path=@_ makes a factor 4.5 performance boost...

      Wow. I'm amazed that avoiding the copying of such a small array had such a dramatic affect on the performance. I guess it must be being copied very many times.

      In mine, I tried building the hash from the array rather than carrying it around, and it produced an ~8% speed-up. Then I tried using $_[n] instead of named parameters and it leached less than 5% more. The first is worth having, the second not:

      sub _findPaths3 { return $_[0]->( @{ $_[4] }, $_[3] ) if $_[2] eq $_[3]; my %seen; $seen{ $_ } = 1 for @{ $_[4] }, $_[2]; for ( grep !$seen{ $_ }, @{ $_[1]->{ $_[2] } } ) { _findPaths3( $_[0], $_[1], $_, $_[3], [ @{ $_[4] }, $_[2] ] ), } } sub findPaths3(&@) { _findPaths3( @_, [] ); }

      Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
      "Science is about questioning the status quo. Questioning authority".
      In the absence of evidence, opinion is indistinguishable from prejudice.
        yep just try to imagine what linearizing and short circuiting could achieve.

        Cheers Rolf

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