Nested Intervals Tree Encoding with Continued Fractions: Difference between revisions
Created page with "Title: Nested Intervals Tree Encoding with Continued Fractions Research Question: How can we improve tree encoding with nested intervals by using continued fractions? Methodology: The authors proposed a new variation of tree encoding with nested intervals, focusing on the connection with materialized path and suggesting a method for moving parts of the hierarchy. They used continued fractions to create a more efficient and flexible encoding schema. Results: The author..." |
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Title: Nested Intervals Tree Encoding with Continued Fractions | Title: Nested Intervals Tree Encoding with Continued Fractions | ||
Research Question: How can we | Research Question: How can we create a more efficient and scalable tree encoding method that combines the advantages of both Materialized Path and Nested Sets, while also addressing their respective drawbacks? | ||
Methodology: | Methodology: | ||
1. Introduction: The authors introduce the concept of Nested Intervals Tree Encoding, a tree encoding method that allows for flexible labeling of tree nodes with rational numbers. They discuss the advantages and disadvantages of existing tree encoding methods, such as Materialized Path and Nested Sets. | |||
2. Continued Fractions: The authors introduce the concept of Continued Fractions, a method used to convert a rational number into a sequence of integers. This method is crucial for mapping tree nodes to Materialized Paths and vice versa. | |||
Link to Article: https://arxiv.org/abs/ | 3. Encoding with Continued Fractions: The authors propose a new tree encoding method that uses Continued Fractions to map tree nodes to Materialized Paths and vice versa. This method allows for efficient querying of tree nodes and ranges, while also addressing the scalability issues of existing methods. | ||
4. Results: The authors provide examples and case studies that demonstrate the effectiveness and efficiency of their proposed method. They show that it can be used to create a more scalable and efficient tree encoding method that combines the advantages of both Materialized Path and Nested Sets. | |||
5. Implications: The authors discuss the implications of their proposed method, including its potential applications in various fields and its impact on the existing tree encoding methods. They also provide suggestions for future research and improvements to their method. | |||
Conclusion: In conclusion, the authors have proposed a new tree encoding method that combines the advantages of both Materialized Path and Nested Sets, while also addressing their respective drawbacks. This method uses Continued Fractions to map tree nodes to Materialized Paths and vice versa, resulting in an efficient and scalable tree encoding method. | |||
Link to Article: https://arxiv.org/abs/0402051v2 | |||
Authors: | Authors: | ||
arXiv ID: | arXiv ID: 0402051v2 | ||
[[Category:Computer Science]] | [[Category:Computer Science]] | ||
[[Category:Tree]] | |||
[[Category:Method]] | |||
[[Category:Encoding]] | [[Category:Encoding]] | ||
[[Category: | [[Category:Materialized]] | ||
[[Category:Nested]] | [[Category:Nested]] | ||
Latest revision as of 15:27, 24 December 2023
Title: Nested Intervals Tree Encoding with Continued Fractions
Research Question: How can we create a more efficient and scalable tree encoding method that combines the advantages of both Materialized Path and Nested Sets, while also addressing their respective drawbacks?
Methodology:
1. Introduction: The authors introduce the concept of Nested Intervals Tree Encoding, a tree encoding method that allows for flexible labeling of tree nodes with rational numbers. They discuss the advantages and disadvantages of existing tree encoding methods, such as Materialized Path and Nested Sets.
2. Continued Fractions: The authors introduce the concept of Continued Fractions, a method used to convert a rational number into a sequence of integers. This method is crucial for mapping tree nodes to Materialized Paths and vice versa.
3. Encoding with Continued Fractions: The authors propose a new tree encoding method that uses Continued Fractions to map tree nodes to Materialized Paths and vice versa. This method allows for efficient querying of tree nodes and ranges, while also addressing the scalability issues of existing methods.
4. Results: The authors provide examples and case studies that demonstrate the effectiveness and efficiency of their proposed method. They show that it can be used to create a more scalable and efficient tree encoding method that combines the advantages of both Materialized Path and Nested Sets.
5. Implications: The authors discuss the implications of their proposed method, including its potential applications in various fields and its impact on the existing tree encoding methods. They also provide suggestions for future research and improvements to their method.
Conclusion: In conclusion, the authors have proposed a new tree encoding method that combines the advantages of both Materialized Path and Nested Sets, while also addressing their respective drawbacks. This method uses Continued Fractions to map tree nodes to Materialized Paths and vice versa, resulting in an efficient and scalable tree encoding method.
Link to Article: https://arxiv.org/abs/0402051v2 Authors: arXiv ID: 0402051v2