Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
O(n2.5) time algorithms for the subgraph homeomorphism problem on trees
Journal of Algorithms
Simple fast algorithms for the editing distance between trees and related problems
SIAM Journal on Computing
On query languages for the P-string data model
Information modelling and knowledge bases
On the complexity of finding iso- and other morphisms for partial k-trees
Discrete Mathematics - Topological, algebraical and combinatorial structures; Froli´k's memorial volume
Retrieval from hierarchical texts by partial patterns
SIGIR '93 Proceedings of the 16th annual international ACM SIGIR conference on Research and development in information retrieval
Ordered and Unordered Tree Inclusion
SIAM Journal on Computing
Ambivalent Data Structures for Dynamic 2-Edge-Connectivity and k Smallest Spanning Trees
SIAM Journal on Computing
More efficient algorithm for ordered tree inclusion
Journal of Algorithms
Time and space efficient method-lookup for object-oriented programs
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Tree pattern matching and subset matching in deterministic O(n log3 n)-time
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
The Tree-to-Tree Correction Problem
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Journal of Algorithms
Querying and ranking XML documents
Journal of the American Society for Information Science and Technology - XML
Journal of Algorithms
Improved labeling scheme for ancestor queries
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Acta Informatica
Maintaining Center and Median in Dynamic Trees
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Fully Persistent Arrays (Extended Array)
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Minimizing Diameters of Dynamic Trees
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
A New Algorithm for the Ordered Tree Inclusion Problem
CPM '97 Proceedings of the 8th Annual Symposium on Combinatorial Pattern Matching
Efficient Dynamic Method-Lookup for Object Oriented Languages (Extended Abstract)
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Computing the Edit-Distance between Unrooted Ordered Trees
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Space efficient dynamic stabbing with fast queries
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
TreeFinder: a First Step towards XML Data Mining
ICDM '02 Proceedings of the 2002 IEEE International Conference on Data Mining
Finding hot query patterns over an XQuery stream
The VLDB Journal — The International Journal on Very Large Data Bases
A survey on tree edit distance and related problems
Theoretical Computer Science
Efficient mining of XML query patterns for caching
VLDB '03 Proceedings of the 29th international conference on Very large data bases - Volume 29
Efficient tree pattern matching
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
The tree inclusion problem: in optimal space and faster
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
An optimal decomposition algorithm for tree edit distance
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Faster bit-parallel algorithms for unordered pseudo-tree matching and tree homeomorphism
Journal of Discrete Algorithms
The Substitution Principle in an Object-Oriented Framework for Web Services: From Failure to Success
Proceedings of International Conference on Information Integration and Web-based Applications & Services
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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 [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. Let nS, lS, and dS denote the number of nodes, the number of leaves, and the depth of a tree S ∈ P, T. In this article we show that the tree inclusion problem can be solved in space O(nT) and time: O⎛⎝min⎧⎨⎩lPnTlPlT log log nT + nTnPnTlog nT+ nT log nT⎫⎬⎭⎞⎠. This improves or matches the best known time complexities while using only linear space instead of quadratic. This is particularly important in practical applications, such as XML databases, where the space is likely to be a bottleneck.