Hello everybody. I need to find all the cycles in a directed graph. For example: A->B->C->A I know about some algorithms as used by Donald B. Johnson, Chang Liu and Lu Ruan, Tarjan, Gabows or Kosaraju and so on, but does anyone know a ruby implementation of any of this algorithms? Actually, I'm using the Ruby Graph Library (RGL), but its not efficient (O(n^4)... it last 10 to 15 minutes to find the cycles in a graph with 33000 edges). Thanks in advance.

on 2010-10-09 18:21

on 2010-10-10 02:25

On 10/09/2010 11:21 AM, NoÃ© Alejandro wrote: > (O(n^4)... it last 10 to 15 minutes to find the cycles in a graph with > 33000 edges). > > Thanks in advance. Hi. I'm sort of the de facto maintainer of RGL these days since the original author (Horst DuchÃªne) left the Ruby community and transitioned to Groovy. RGL, in fact, uses Tarjan's algorithm for detection of strongly connected components: http://rdoc.info/gems/rgl/0.4.0/RGL/Graph#strongly... Horst wrote that code, and I have an application that uses the functionality frequently, although with graphs that have significantly fewer than 33,000 edges. How did you come to the conclusion that the complexity of RGL's implementation is O(n^4)? The implementation should be O(|V||E|) assuming Tarjan's algorithm is properly implemented, but I admit that I haven't performed an examination of RGL's implementation personally. -Jeremy

on 2010-10-10 03:27

Jeremy Bopp wrote: > On 10/09/2010 11:21 AM, NoÃ© Alejandro wrote: >> (O(n^4)... it last 10 to 15 minutes to find the cycles in a graph with >> 33000 edges). >> >> Thanks in advance. > > Hi. I'm sort of the de facto maintainer of RGL these days since the > original author (Horst DuchÃªne) left the Ruby community and transitioned > to Groovy. > > RGL, in fact, uses Tarjan's algorithm for detection of strongly > connected components: > > http://rdoc.info/gems/rgl/0.4.0/RGL/Graph#strongly... > > Horst wrote that code, and I have an application that uses the > functionality frequently, although with graphs that have significantly > fewer than 33,000 edges. How did you come to the conclusion that the > complexity of RGL's implementation is O(n^4)? The implementation should > be O(|V||E|) assuming Tarjan's algorithm is properly implemented, but I > admit that I haven't performed an examination of RGL's implementation > personally. > > -Jeremy Hello Jeremy, nice to meet you. Well, I came to that conclusion because that is what documentation says: http://rgl.rubyforge.org/rgl/classes/RGL/MutableGr... cycles() Returns an array of all minimum cycles in a graph. This is not an efficient implementation O(n^4)... At least that was I understood. Greetings.

on 2010-10-10 06:10

On 10/09/2010 08:27 PM, NoÃ© Alejandro wrote: > Hello Jeremy, nice to meet you. > > Well, I came to that conclusion because that is what documentation says: > http://rgl.rubyforge.org/rgl/classes/RGL/MutableGr... > > cycles() > Returns an array of all minimum cycles in a graph. > This is not an efficient implementation O(n^4)... > > At least that was I understood. I see. Do you need the minimum cycles passing through each vertex of the graph, or is it sufficient that you identify the clusters of vertexes which participate in one or more interconnected cycles? For instance, say you have the following graph: A -> B -> C -> A A -> D -> E -> A A -> F -> G The minimum cycles should be: [A, B, C] [A, D, E] However, the strongly connected components would be: [A, B, C, D, E] [F] [G] You could then filter out the trivial components that contain only a single vertex; however, doing so will hide any vertexes that point back to themselves directly. The strongly connected component computation is much more efficient at the moment apparently, so if you think that might satisfy your needs, you should give it try: require 'rgl/connected_components' inv_comp_map = {} # g is your graph instance... g.strongly_connected_components.comp_map.each do |v, n| (inv_comp_map[n] ||= []) << v end # This will yield a list of lists of vertexes representing # the non-trivial strongly connected components of the graph. inv_comp_map.values.delete_if { |scc| scc.size == 1 } I wish that the strongly_connected_components method automatically returned a ready-to-use list of the strongly connected components rather than the TarjanSccVisitor instance used to compute the list. Unfortunately, due to ongoing discussions with my employer, I'm not able to publish any code myself at the moment, but I'm more than happy to accept patches from others. :-) -Jeremy