@@ -34,7 +34,7 @@ Choose one of the following project themes for the **design and analysis phase**
Space partitioning algorithms represent a category of specialized data structures often used to solve two key problems in [computational geometry](https://www.algorist.com/sections/Computational_Geometry.html): [nearest neighbor search](https://www.algorist.com/problems/Nearest_Neighbor_Search.html) and [range search](https://www.algorist.com/problems/Range_Search.html). These operations provide efficient algorithms for [swarm intelligence](https://jumpoffboids.netlify.app/), [*N*-body simulation](https://en.wikipedia.org/wiki/N-body_simulation), and [non-parametric classification](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm).
Space partitioning often assumes multi-dimensional data: our input data is not just a set of values, but a set of points in a multi-dimensional space. For example, a datapoints in 3-dimensional space could be represented by datapoints with *x*, *y*, and *z* values. For an introduction to space partitioning algorithms, watch the UC Berkeley lecture on [Multidimensional Data](https://www.youtube.com/playlist?list=PL8FaHk7qbOD4F7nPFfgD0dGdLos1uhUPg)([slides](https://docs.google.com/presentation/d/1b3DAvlP1jDw-6KYOVVDxbIsg1Y3DcRWEbx1hE2J0gO8/edit?usp=sharing)) and study the Princeton slides on [Geometric Applications of BSTs](https://www.cs.princeton.edu/courses/archive/fall20/cos226/lectures/99GeometricSearch.pdf).
Space partitioning often assumes multi-dimensional data: our input data is not just a set of values, but a set of datapoints in a multi-dimensional space. For example, a set of datapoints in 3-dimensional space could be represented by datapoints with *x*, *y*, and *z* values. For an introduction to space partitioning algorithms, watch the UC Berkeley lecture on [Multidimensional Data](https://www.youtube.com/playlist?list=PL8FaHk7qbOD4F7nPFfgD0dGdLos1uhUPg)([slides](https://docs.google.com/presentation/d/1b3DAvlP1jDw-6KYOVVDxbIsg1Y3DcRWEbx1hE2J0gO8/edit?usp=sharing)) and study the Princeton slides on [Geometric Applications of BSTs](https://www.cs.princeton.edu/courses/archive/fall20/cos226/lectures/99GeometricSearch.pdf).
1.[K-d trees](https://www.algorist.com/problems/Kd-Trees.html)([2-d tree demo](https://www.cs.princeton.edu/courses/archive/fall20/cos226/demos/99DemoKdTree/index.html))
