Class AHUForestIsomorphismInspector<V,E>

Type Parameters:
V - the type of the vertices
E - the type of the edges
All Implemented Interfaces:

public class AHUForestIsomorphismInspector<V,E> extends Object implements IsomorphismInspector<V,E>
This is an implementation of the AHU algorithm for detecting an (unweighted) isomorphism between two rooted forests. Please see for a complete definition of the isomorphism problem for general graphs.

The original algorithm was first presented in "Alfred V. Aho and John E. Hopcroft. 1974. The Design and Analysis of Computer Algorithms (1st ed., page 84). Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA."

This implementation runs in linear time (in the number of vertices of the input forests) while using a linear amount of memory.

For an implementation that supports rooted trees see AHURootedTreeIsomorphismInspector and for one for unrooted trees see AHUUnrootedTreeIsomorphismInspector.

Note: This implementation requires the input graphs to have valid vertex suppliers (see Graph.getVertexSupplier()).

Note: This inspector only returns a single mapping (chosen arbitrarily) rather than all possible mappings.

Alexandru Valeanu
  • Constructor Details

    • AHUForestIsomorphismInspector

      public AHUForestIsomorphismInspector(Graph<V,E> forest1, Set<V> roots1, Graph<V,E> forest2, Set<V> roots2)
      Construct a new AHU rooted forest isomorphism inspector. Note: The constructor does NOT check if the input forests are valid trees.
      forest1 - the first rooted forest
      roots1 - the roots of the first forest
      forest2 - the second rooted forest
      roots2 - the roots of the second forest
      NullPointerException - if forest1 or forest2 is null
      NullPointerException - if roots1 or roots2 is null
      IllegalArgumentException - if forest1 or forest2 is empty
      IllegalArgumentException - if roots1 or roots2 is empty
      IllegalArgumentException - if roots1 or roots2 contain an invalid vertex
  • Method Details

    • getMappings

      public Iterator<GraphMapping<V,E>> getMappings()
      Get an iterator over all calculated (isomorphic) mappings between two graphs.
      Specified by:
      getMappings in interface IsomorphismInspector<V,E>
      an iterator over all calculated (isomorphic) mappings between two graphs
    • isomorphismExists

      public boolean isomorphismExists()
      Check if an isomorphism exists.
      Specified by:
      isomorphismExists in interface IsomorphismInspector<V,E>
      true if there is an isomorphism, false if there is no isomorphism
    • getMapping

      public IsomorphicGraphMapping<V,E> getMapping()
      Get an isomorphism between the input forests or null if none exists.
      isomorphic mapping, null is none exists