Nested Intervals Tree Encoding with Continued Fractions

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 authors found that continued fractions can be interpreted as nested intervals, allowing for a simpler and more efficient encoding schema. They also demonstrated that this new schema is compatible with materialized path, providing a clear connection between the two methods.

Implications: The use of continued fractions in tree encoding with nested intervals has several implications. First, it improves the scalability of the encoding schema, making it suitable for larger tree structures. Second, it simplifies the process of moving parts of the hierarchy, making the encoding schema more user-friendly. Lastly, the connection with materialized path provides a new perspective on tree encoding, potentially leading to further advancements in the field.

Link to Article: https://arxiv.org/abs/0402051v1 Authors: arXiv ID: 0402051v1