The Tree Inclusion Problem: In Optimal Space and Faster

TR-2005-54, Authors: Philip Bille and Inge Li Gørtz

Philip Bille
Inge Li Gørtz

January 2005

Abstract

Given two rooted, ordered, and labeled trees P and T the tree inclusion problem is to determine if P can be obtained from T by deleting nodes in T. This problem has recently been recognized as an important query primitive in XML databases.Kilpeläinen and Mannila (SIAM J. of Comp. 1995) presented the first polynomial time algorithm using quadratic time and space. Since then several improved results have been obtained for special cases when P and T have a small number of leaves or small depth. However, in the worst case these algorithms still use quadratic time and space. In this paper we present a new approach to the problem which leads to a new algorithm which use optimal linear space and has subquadratic running time. Our algorithm improves all previous time and space bounds.Most importantly, the space is improved by a linear factor. This will make it possible to query larger XML databases and speed up the query time since more of the computation can be kept in main memory.

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Technical report TR-2005-54 in IT University Technical Report Series,
January 2005.

Available as PDF.