Group-Theoretical Perspective of Tree Editing

Tree Editing Distance is a widely applied quantity for measuring the similarity between hierarchical data structures, particularly trees. This paper reinterprets the TED problem using group action theory, exploring the connection between tree editing operations and permutation groups. By formulating node insertion, deletion, and relabeling as group actions, we offer a novel perspective on tree transformations. This group-theoretic and metric-based approach provides new insights into the structure of tree similarity and introduces new possibilities for TED applications in various fields.