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Fix broken links (#378)
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JosepSampe committed Aug 5, 2024
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2 changes: 1 addition & 1 deletion CONTRIBUTING.md
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Expand Up @@ -334,7 +334,7 @@ Example: `0.6.2-badfbadf-SNAPSHOT`
# Licensing of contributed material
All contributed code, docs, and other materials are considered licensed under the same terms as the rest of the project. Check [LICENSE](./LICENCE) for more details.
All contributed code, docs, and other materials are considered licensed under the same terms as the rest of the project. Check [LICENSE](./LICENSE) for more details.
# Community Values
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2 changes: 1 addition & 1 deletion docs/OTreeAlgorithm.md
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Expand Up @@ -8,7 +8,7 @@ The two primary goals of the **OTree algorithm** are
### Recursive Space Division
One of the most important techniques used to build a **multi-dimensional index** is through **recursive space division**; a bounded vector space initially containing all the data is **recursively divided** into **equal-sized**, **non-overlapping** subspaces, as long as they exceed the predefined **capacity**.

For a dataset indexed with `n` columns, the constructed index is an n-dimensional vector space composed of <img src="https://render.githubusercontent.com/render/math?math=2^n" /> subspaces, or what we call `cubes`, with **non-overlapping** boundaries. Each cube can contain a predefined number of element `cap`, and exceeding it would trigger **recursively dividing** a cube into child cubes by halving the ranges in all dimensions until the number of elements included no longer exceeds `cap`.
For a dataset indexed with `n` columns, the constructed index is an n-dimensional vector space composed of $2^n$ subspaces, or what we call `cubes`, with **non-overlapping** boundaries. Each cube can contain a predefined number of element `cap`, and exceeding it would trigger **recursively dividing** a cube into child cubes by halving the ranges in all dimensions until the number of elements included no longer exceeds `cap`.

Say that we use two columns, `x`, and `y` to build the index, and the parameter cap for each cube is 2. The first image in the figure below is the **root cube**, containing more than two elements. The cube is split into four **equal-sized**, **non-overlapping** child cubes with one space division step, as shown in the middle image. Three of the four cubes are in good condition as a result of the division.

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