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# Dualities in Tree Representations

1 BONSAI - Bioinformatics and Sequence Analysis
Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189, CNRS - Centre National de la Recherche Scientifique
Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01935566
Contributor : Rayan Chikhi <>
Submitted on : Monday, November 26, 2018 - 6:01:16 PM
Last modification on : Friday, April 19, 2019 - 4:55:21 PM

### Identifiers

• HAL Id : hal-01935566, version 1
• ARXIV : 1804.04263

### Citation

Rayan Chikhi, Alexander Schönhuth. Dualities in Tree Representations. 2018. ⟨hal-01935566⟩

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