Module org.jgrapht.core
Package org.jgrapht.alg.similarity

Class ZhangShashaTreeEditDistance<V,E>

java.lang.Object
org.jgrapht.alg.similarity.ZhangShashaTreeEditDistance<V,E>
Type Parameters:
V - graph vertex type
E - graph edge type
public class ZhangShashaTreeEditDistance<V,E> extends Object
Dynamic programming algorithm for computing edit distance between trees.

The algorithm is originally described in Zhang, Kaizhong & Shasha, Dennis. (1989). Simple Fast Algorithms for the Editing Distance Between Trees and Related Problems. SIAM J. Comput.. 18. 1245-1262. 10.1137/0218082.

The time complexity of the algorithm is $O(|T_1|\cdot|T_2|\cdot min(depth(T_1),leaves(T_1)) \cdot min(depth(T_2),leaves(T_2)))$. Space complexity is $O(|T_1|\cdot |T_2|)$, where $|T_1|$ and $|T_2|$ denote number of vertices in trees $T_1$ and $T_2$ correspondingly, $leaves()$ function returns number of leaf vertices in a tree.

The tree edit distance problem is defined in a following way. Consider $2$ trees $T_1$ and $T_2$ with root vertices $r_1$ and $r_2$ correspondingly. For those trees there are 3 elementary modification actions:

  • Remove a vertex $v$ from $T_1$.
  • Insert a vertex $v$ into $T_2$.
  • Change vertex $v_1$ in $T_1$ to vertex $v_2$ in $T_2$.
The algorithm assigns a cost to each of those operations which also depends on the vertices. The problem is then to compute a sequence of edit operations which transforms $T_1$ into $T_2$ and has a minimum cost over all such sequences. Here the cost of a sequence of edit operations is defined as sum of costs of individual operations.

The algorithm is based on a dynamic programming principle and assigns a label to each vertex in the trees which is equal to its index in post-oder traversal. It also uses a notion of a keyroot which is defined as a vertex in a tree which has a left sibling. Additionally a special $l()$ function is introduced with returns for every vertex the index of its leftmost child wrt the post-order traversal in the tree.

Solving the tree edit problem distance is divided into computing edit distance for every pair of subtrees rooted at vertices $v_1$ and $v_2$ where $v_1$ is a keyroot in the first tree and $v_2$ is a keyroot in the second tree.

  • Field Details

    • tree1

      private Graph<V,E> tree1
      First tree for which the distance is computed by this algorithm.

    • root1

      private V root1
      Root vertex of the tree1.

    • tree2

      private Graph<V,E> tree2
      Second tree for which the distance is computed by this algorithm.

    • root2

      private V root2
      Root vertex of the tree2.

    • insertCost

      private ToDoubleFunction<V> insertCost
      Function which computes cost of inserting a particular vertex into tree2.

    • removeCost

      private ToDoubleFunction<V> removeCost
      Function which computes cost of removing a particular vertex from {2code tree1}.

    • changeCost

      private ToDoubleBiFunction<V,V> changeCost
      Function which computes cost of changing a vertex $v1$ in tree1 to vertex $v2$ in tree2.

    • treeDistances

      private double[][] treeDistances
      Array with edit distances between subtrees of tree1 and tree2. Formally, $treeDistances[i][j]$ stores edit distance between subtree of tree1 rooted at vertex $i+1$ and subtree of tree2 rooted at vertex $j+1$, where $i$ and $j$ are vertex indices from the corresponding tree orderings.

    • editOperationLists

      private List<List<List<ZhangShashaTreeEditDistance.EditOperation<V>>>> editOperationLists
      Array with lists of edit operations which transform subtrees of tree1 into subtrees tree2. Formally, editOperationLists[i][j]$ stores a list of edit operations which transform subtree tree1 rooted at vertex $i$ into subtree of tree2 rooted at vertex $j$, where $i$ and $j$ are vertex indices from the corresponding tree orderings.

    • algorithmExecuted

      private boolean algorithmExecuted
      Helper field which indicates whether the algorithm has already been executed for tree1 and tree2.

  • Constructor Details

    • ZhangShashaTreeEditDistance

      public ZhangShashaTreeEditDistance(Graph<V,E> tree1, V root1, Graph<V,E> tree2, V root2)
      Constructs an instance of the algorithm for the given tree1, root1, tree2 and root2. This constructor sets following default values for the distance functions. The insertCost and removeCost always return $1.0$, the changeCost return $0.0$ if vertices are equal and 1.0 otherwise.
      Parameters:
      tree1 - a tree
      root1 - root vertex of tree1
      tree2 - a tree
      root2 - root vertex of tree2

    • ZhangShashaTreeEditDistance

      public ZhangShashaTreeEditDistance(Graph<V,E> tree1, V root1, Graph<V,E> tree2, V root2, ToDoubleFunction<V> insertCost, ToDoubleFunction<V> removeCost, ToDoubleBiFunction<V,V> changeCost)
      Constructs an instance of the algorithm for the given tree1, root1, tree2, root2, insertCost, removeCost and changeCost.
      Parameters:
      tree1 - a tree
      root1 - root vertex of tree1
      tree2 - a tree
      root2 - root vertex of tree2
      insertCost - cost function for inserting a node into tree1
      removeCost - cost function for removing a node from tree2
      changeCost - cost function of changing a node in tree1 to a node in tree2

  • Method Details

    • getDistance

      public double getDistance()
      Computes edit distance for tree1 and tree2.
      Returns:
      edit distance between tree1 and tree2

    • getEditOperationLists

      public List<ZhangShashaTreeEditDistance.EditOperation<V>> getEditOperationLists()
      Computes a list of edit operations which transform tree1 into tree2.
      Returns:
      list of edit operations

    • lazyRunAlgorithm

      private void lazyRunAlgorithm()
      Performs lazy computations of this algorithm and stores cached data in treeDistances and editOperationList.

    • treeDistance

      private void treeDistance(int i, int j, ZhangShashaTreeEditDistance<V,E>.TreeOrdering ordering1, ZhangShashaTreeEditDistance<V,E>.TreeOrdering ordering2)
      Computes edit distance and list of edit operations for vertex $v1$ from tree1 which has tree ordering index equal to $i$ and vertex $v2$ from tree2 which has tree ordering index equal to $j$. Both $v1$ and $v2$ must be keyroots in the corresponding trees.
      Parameters:
      i - ordering index of a keyroot in tree1
      j - ordering index of a keywoot in tree2
      ordering1 - ordering of tree1
      ordering2 - ordering of tree2

    • restoreOperationsList

      private List<ZhangShashaTreeEditDistance.EditOperation<V>> restoreOperationsList(List<List<ZhangShashaTreeEditDistance<V,E>.CacheEntry>> cachedOperations, int i, int j)
      Restores list of edit operations which have been cached in cachedOperations during the edit distance computation. Starting from a cache entry at index $(i,j)$.
      Parameters:
      cachedOperations - 2-dimensional list with cached operations
      i - starting operation index
      j - starting operation index
      Returns:
      list of edit operations