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 [1]. For unordered trees the problem of finding a maximum-weight Tai mapping is known to be NP-complete [2]. 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 $(x,y),(x^{\prime },y^{\prime })\in M$ violate ancestor relationship and thus cannot be part of the same Tai mapping, i.e. $(x\le x^{\prime }\iff y\nleqq y^{\prime })\vee (x^{\prime }\le x\iff y^{\prime }\nleqq y)$, given an ancestor order $x<x^{\prime }$ meaning that x is an ancestor of $x^{\prime }$. Finding a maximum-weight anti Tai mapping arises in the cutting plane method for solving the maximum-weight Tai mapping problem via integer programming. We give an efficient polynomial-time algorithm for finding a maximum-weight anti Tai mapping for the case when one of the two trees is a path and further show how to extend this result in order to provide a polynomially computable lower bound on the optimal anti Tai mapping for two unordered labeled trees. The latter result stems from the special class of anti Tai mappings defined by the more restricted condition $x\sim x^{\prime }\iff y\nsim y^{\prime }$, where ∼ denotes that two nodes belong to the same root-to-leaf path. For this class, we give an efficient algorithm that solves the problem exactly on two unordered trees in $O(|V_1{|}^2|V_2{|}^2)$.

两个有根标记树之间经过充分研究的 Tai 映射${\mathrm{时间}}_1=（V_1,{乙}_1）$和${\mathrm{时间}}_2=（V_2,{乙}_2）$定义了节点之间的一对一映射${\mathrm{时间}}_1$和${\mathrm{时间}}_2$保留祖先关系[1]。对于无序树，找到最大权重 Tai 映射的问题已知是 NP 完全问题[2]。在这项工作中，我们定义了一个反 Tai 映射$\mathrm{中号}\subseteq V_1\times V_2$作为两个无序标记树之间的二元关系，使得任意两个$（X,y）,（X^{\prime },y^{\prime }）\epsilon \mathrm{中号}$违反祖先关系，因此不能是同一 Tai 映射的一部分，即$（X\le X^{\prime }\iff y\nleqq y^{\prime }）\vee （X^{\prime }\le X\iff y^{\prime }\nleqq y）$，给定祖先顺序$X<X^{\prime }$意味着x是$X^{\prime }$。寻找最大权值反Tai映射是在通过整数规划求解最大权值Tai映射问题的割平面方法中出现的。我们给出了一种有效的多项式时间算法，用于在两棵树之一是路径的情况下找到最大权重抗 Tai 映射，并进一步展示如何扩展此结果，以便提供最优抗的多项式可计算下界两个无序标记树的 Tai 映射。后一个结果源于由更严格的条件定义的特殊类别的反 Tai 映射$X～X^{\prime }\iff y\nsim y^{\prime }$，其中 ∼ 表示两个节点属于同一根到叶路径。对于此类，我们给出了一种有效的算法，可以精确地解决两棵无序树上的问题$氧（|V_1{|}^2|V_2{|}^2）$。