An algebraic view of the relation between largest common subtrees and smallest common supertrees

Authors:
Francesc Rosselló;Gabriel Valiente
Affiliations:
Department of Mathematics and Computer Science, Research Institute of Health Science (IUNICS), University of the Balearic Islands, Palma de Mallorca, Spain;Algorithms, Bioinformatics, Complexity and Formal Methods Research Group, Department of Software, Technical University of Catalonia, Barcelona, Spain
Venue:
Theoretical Computer Science
Year:
2006

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Abstract

The relationship between two important problems in tree pattern matching, the largest common subtree and the smallest common supertree problems, is established by means of simple constructions, which allow one to obtain a largest common subtree of two trees from a smallest common supertree of them, and vice versa. These constructions are the same for isomorphic, homeomorphic, topological, and minor embeddings, they take only time linear in the size of the trees, and they turn out to have a clear algebraic meaning.