Partial subtree-matching algorithm

Question

I searched the forums but I couldn\'t figure it out if the other similar questions are necessarily related to this one.

What I\'m trying to do is match a subtree to a t

Answer 1

It appears that what I was looking for was an algorithm to solve the "tree inclusion problem". I have found some useful documents:

Fast Algorithms for Finding Nearest Common Ancestors

The Tree Inclusion Problem: In Optimal Space and Faster

Tree Isomorphism And Related Problems

I translated one of the algorithms from the last paper into C# (returns the number of pairs in a largest matching between first-level subtrees of a and b).

public static int Match(Node a, Node b, NodeSimilarityComparer comp) {
  if (!comp.Equals(a, b))
    return 0;
  int m = a.SubtreeCount;
  int n = b.SubtreeCount;
  var matrix = new int[m + 1, n + 1];

  for (int i = 0; i <= m; ++i)
    matrix[i, 0] = 0;

  for (int j = 0; j <= n; ++j)
    matrix[0, j] = 0;

  for (int i = 1; i <= m; ++i)
    for (int j = 1; j <= n; ++j) {
      var ai = a.GetSubtree(i - 1);
      var bj = b.GetSubtree(j - 1);
      var match = Match(ai, bj, comp);
      matrix[i, j] = Math.Max(Math.Max(matrix[i, j - 1], matrix[i - 1, j]), matrix[i - 1, j - 1] + match);
    }
  return matrix[m, n] + 1;
}

Hope this helps others too.