New and improved algorithms for unordered tree inclusion

The tree inclusion problem is, given two node-labeled trees P and T (the “pattern tree” the “target tree”), to locate every minimal subtree in (if any) that can be obtained by applying a sequence of node insertion operations P. Although ordered is solvable polynomial time, unordered NP-hard. currently fastest algorithm for latter classic Kilpeläinen Mannila from 1995 runs O(d22dmn) where m n are sizes pattern target trees, respectively, d degree tree. Here, we develop new O(d2dmn2) improving exponential factor 22d 2d considering particular type ancestor-descendant relationships suitable dynamic programming. We also study restricted variants problem.