树表示中的对偶
Dualities in Tree Representations
摘要：
给出了树$T^*$的一个特征，使得$\mathrm{BP}(T^*)=\overleftrightarrow{\mathrm{DFUDS}(T)}$是$\mathrm{DFUDS}(T)$的逆.一个直接的结果是树$\hat{T}$的严格表征，使得$\mathrm{BP}(\hat{T})=\mathrm{DFUDS}(T)$。总之，$\mathrm{BP}$和$\mathrm{DFUDS}$在一个包含框架内是统一的，这可能意味着未来对$\mathrm{BP}$和/或$\mathrm{DFUDS}$中的查询进行简化。这里显示的直接好处是识别到目前为止未注意到的共性在最近的工作范围最小查询问题，并提供最小长度间隔查询问题的改进。
英文摘要：
A characterization of the tree $T^*$ such that $\mathrm{BP}(T^*)=\overleftrightarrow{\mathrm{DFUDS}(T)}$, the reversal of $\mathrm{DFUDS}(T)$ is given. An immediate consequence is a rigorous characterization of the tree $\hat{T}$ such that $\mathrm{BP}(\hat{T})=\mathrm{DFUDS}(T)$. In summary, $\mathrm{BP}$ and $\mathrm{DFUDS}$ are unified within an encompassing framework, which might have the potential to imply future simplifications with regard to queries in $\mathrm{BP}$ and/or $\mathrm{DFUDS}$. Immediate benefits displayed here are to identify so far unnoted commonalities in most recent work on the Range Minimum Query problem, and to provide improvements for the Minimum Length Interval Query problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
