Automorphism generation algorithm

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Problem




Given a rooted tree T, i need to iterate over the automorphism group
aut(T), that is the set of all node permutation resulting in an
isomorphic version of T.




E.g. let T be a "cherry": root is connected with 2 children (total 3 nodes and 2 edges). Then aut(T)=(1,2,3)=id,(1,3,2) if the root has the identifier 1.



Algorithms i tried




  1. 'Naive'



    Iterate over the permuation group Pn (all possible permutations of the nodes) and check for each if the permuation is a valid automorphism.
    => runtime O(n!*m) with n the number of nodes of T and m the number of edges of T.




  2. Set of generators using bliss



    I tried using the find_automorphisms_generators function of bliss library, but this is not very helpful, since i have to compute all possible combinations of such generators to obtain the full set of automorphisms. This take a lot of time although the find_automorphisms_generators is very fast...



Question:




Is there any library/function optimized for rooted trees? (i use c++
but i can adapt to anything)





graph-theory automorphism-group




share|cite|improve this question























    up vote
    1
    down vote

    favorite












    Problem




    Given a rooted tree T, i need to iterate over the automorphism group
    aut(T), that is the set of all node permutation resulting in an
    isomorphic version of T.




    E.g. let T be a "cherry": root is connected with 2 children (total 3 nodes and 2 edges). Then aut(T)=(1,2,3)=id,(1,3,2) if the root has the identifier 1.



    Algorithms i tried




    1. 'Naive'



      Iterate over the permuation group Pn (all possible permutations of the nodes) and check for each if the permuation is a valid automorphism.
      => runtime O(n!*m) with n the number of nodes of T and m the number of edges of T.




    2. Set of generators using bliss



      I tried using the find_automorphisms_generators function of bliss library, but this is not very helpful, since i have to compute all possible combinations of such generators to obtain the full set of automorphisms. This take a lot of time although the find_automorphisms_generators is very fast...



    Question:




    Is there any library/function optimized for rooted trees? (i use c++
    but i can adapt to anything)





    graph-theory automorphism-group




    share|cite|improve this question





















      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      Problem




      Given a rooted tree T, i need to iterate over the automorphism group
      aut(T), that is the set of all node permutation resulting in an
      isomorphic version of T.




      E.g. let T be a "cherry": root is connected with 2 children (total 3 nodes and 2 edges). Then aut(T)=(1,2,3)=id,(1,3,2) if the root has the identifier 1.



      Algorithms i tried




      1. 'Naive'



        Iterate over the permuation group Pn (all possible permutations of the nodes) and check for each if the permuation is a valid automorphism.
        => runtime O(n!*m) with n the number of nodes of T and m the number of edges of T.




      2. Set of generators using bliss



        I tried using the find_automorphisms_generators function of bliss library, but this is not very helpful, since i have to compute all possible combinations of such generators to obtain the full set of automorphisms. This take a lot of time although the find_automorphisms_generators is very fast...



      Question:




      Is there any library/function optimized for rooted trees? (i use c++
      but i can adapt to anything)





      graph-theory automorphism-group




      share|cite|improve this question











      Problem




      Given a rooted tree T, i need to iterate over the automorphism group
      aut(T), that is the set of all node permutation resulting in an
      isomorphic version of T.




      E.g. let T be a "cherry": root is connected with 2 children (total 3 nodes and 2 edges). Then aut(T)=(1,2,3)=id,(1,3,2) if the root has the identifier 1.



      Algorithms i tried




      1. 'Naive'



        Iterate over the permuation group Pn (all possible permutations of the nodes) and check for each if the permuation is a valid automorphism.
        => runtime O(n!*m) with n the number of nodes of T and m the number of edges of T.




      2. Set of generators using bliss



        I tried using the find_automorphisms_generators function of bliss library, but this is not very helpful, since i have to compute all possible combinations of such generators to obtain the full set of automorphisms. This take a lot of time although the find_automorphisms_generators is very fast...



      Question:




      Is there any library/function optimized for rooted trees? (i use c++
      but i can adapt to anything)






      graph-theory automorphism-group





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Aug 1 at 11:23









      Paul

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