Nearest Embedded and Embedding Self-Nested Trees
Abstract
:1. Introduction
2. Preliminaries
2.1. Unordered Rooted Trees
2.2. DAG Compression
2.3. Self-Nested Trees
3. Height Profile of the Tree Structure
3.1. Definition and Complexity
3.2. Relation with Self-Nested Trees
Algorithm 1: Construction of a self-nested tree from its height profile. |
4. Approximation Algorithms
4.1. Definitions
4.1.1. Editing Operations
4.1.2. Constrained Editing Operations
4.1.3. Preserving the Height of the Pre-Existing Nodes
4.1.4. NEST and NeST
- Internal nodes (AI): adding w as a child of v making w the parent of the child c of v can be done only if .
- Subtrees (AS): adding t as a child of v can be done only if .
- Internal nodes (DI): deleting (making the unique child w of v a child of u) can be done only if there exists , , such that .
- Subtrees (DS): deleting the subtree , , of can be done if there exists , , such that .
4.2. NEST Algorithm
Algorithm 2: Construction of the nearest embedding self-nested tree. |
4.3. NeST Algorithm
Algorithm 3: Construction of the nearest embedded self-nested tree. |
5. Numerical Illustration
5.1. Random Trees
5.2. Structural Analysis of a Rice Panicle
6. Summary and Concluding Remarks
Funding
Acknowledgments
Conflicts of Interest
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Azaïs, R. Nearest Embedded and Embedding Self-Nested Trees. Algorithms 2019, 12, 180. https://doi.org/10.3390/a12090180
Azaïs R. Nearest Embedded and Embedding Self-Nested Trees. Algorithms. 2019; 12(9):180. https://doi.org/10.3390/a12090180
Chicago/Turabian StyleAzaïs, Romain. 2019. "Nearest Embedded and Embedding Self-Nested Trees" Algorithms 12, no. 9: 180. https://doi.org/10.3390/a12090180