An Algebraic View of the Relation between Largest Common Subtrees and Smallest Common Supertrees

TL;DR

This paper explores the algebraic relationship between the largest common subtree and smallest common supertree problems in tree pattern matching, providing linear-time constructions applicable to various embedding types.

Contribution

It introduces simple, algebraically meaningful constructions that relate largest common subtrees and smallest common supertrees across multiple embedding types, with linear time complexity.

Findings

Linear-time constructions for relating subtrees and supertrees

Applicability to isomorphic, homeomorphic, topological, and minor embeddings

Clear algebraic interpretation of the relationship

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.