Anti Tai Mapping for Unordered Labeled Trees

The well-studied Tai mapping between two rooted labeled trees $T_1(V_1, E_1)$ and $T_2(V_2, E_2)$ defines a one-to-one mapping between nodes in $T_1$ and $T_2$ that preserves ancestor relationship. For unordered trees the problem of finding a maximum-weight Tai mapping is known to be NP-complete. In this work, we define an anti Tai mapping $M\subseteq V_1\times V_2$ as a binary relation between two unordered labeled trees such that any two $(x,y), (x', y')\in M$ violate ancestor relationship and thus cannot be part of the same Tai mapping, i.e. $(x\le x' \iff y\not \le y') \vee (x'\le x \iff y'\not \le y)$, given an ancestor order $x