A new algorithm for the ordered tree inclusion problem

Abstract

In the problem of ordered tree inclusion two ordered labeled trees P and T are given, and the pattern tree P matches the target tree T at a node x, if there exists a one-to-one map f from the nodes of P to the nodes of T which preserves the labels, the ancestor relation and the left-to-right ordering of the nodes. In [7] Kilpeläinen and Mannila give an algorithm that solves the problem of ordered tree inclusion in time and space ϴ (|P| ·|T|). In this paper we present a new algorithm for the ordered tree inclusion problem with time complexity O(|ΣP| ·|T| + #matches. DEPTH(T)), where ΣP is the alphabet of the labels of the pattern tree and #matches is the number of pairs (v, w) ∈ P × T with LABEL(v) = LABEL(w). The space complexity of our algorithm is O(|ΣP|·|T| + #matches).