Fastest Neighbor Nearest Neighbor (in the) West is an in-development kDtree library that aims to be one of the most, if not the most, performant parallel kNN libraries that exist.
There are several key components of the building and querying process of the kDtrees that allows for its performance.
By using quickselect in the form of rust's select_nth_unstable_by in Rust's core::slice instead of a O(N) average or even some other log(N) median algorithm, we get the left and right subsets for free in the same O(log N) algorithm instead of having to do yet another O(N) comparisons to obtain the left and right bins. As such, the build is still O(N log(N)), but removes this O(N) operation that is found in many libraries.
Many kD-Tree build implementations are not parallel. Every branch (and subbranch) of the tree is an independent kD-tree. After some number of splittings, one could throw the builds of the remaining branches on different threads. This is done here at the user-specified par_split_level, which is the tree depth at which the parallelism begins.
Most libraries return either the kNN distance or the distance and the corresponding data point's index. Here we return the distance, the index, and the neighbor. The way in which we obtain the index is new.
HashMap<&'[NotNan<f64>; D], u64>We attempted to do what other libraries do, which is to flinging around the data's index in some struct or tuple, e.g. &(usize, [NotNan<f64>; D], but found poor performance. By using the ordered_float crate's NotNan<T>, struct, floating points become hashable. Then, one can do all querying operations using just the query and candiate positions, and then do an O(1) lookup at the end to retrieve the closest neighbor's index. This HashMap is constructed at build time in parallel with the tree itself, adding only the overhead of the thread spawn.
I debated about whether I should even mention this one... Because we know the shape of all arrays (i.e. the dimension of the tree) at compile time, the unsafe methods get_unchecked and get_unchecked_mut are used liberally throughout the code. Although the impact of this has not been meausured explicitly, theoretically this means virtually no bounds checks are done. It is possible that LLVM optimizes away lots of the bounds checks anyway. There are also several unwrap_unchecked calls to several Option<T> that are guaranteed by the algorithm to be nonempty. (Going against best practices, these two use cases were pre-optimizations).
At present, the library only serves 1NN queries. In the very near future, this functionality will be expanded to kNN (k>1) queries. In addition, support for periodic boundary conditions will be added. Finally, there are plans to add generic parameters to allow for monomorphization over f32 and f64 (at present only f64 is supported).
This library is intended to be used by the author to calculate summary statistics in cosmology. As such, the parameters of the benchmark chosen are close to those that would be used in analyzing the output of a cosmological simulation. We use - A mock dataset of 100,000 uniform random points in the unit cube. - A query set of 1,000,000 uniform random points in the unit cube.
In such an application, often many subsamples or simulation boxes are used. So, the combined build + query time is important since many different trees may be constructed in an analysis.
Over 100 realizations of the datasets and query points, the following results are obtained for the average build (serial) and 1NN query times on an AMD EPYC 7502P using 48 threads. The results are sorted by the combined build and query time.
| Code | Build (ms)| Query (ms) | Total (ms) | |---|---|---|---| | FNNTW| 11 | 28 | 39 | | pykdtree (python)| 12 | 36 | 48 | | nabo-rs (rust)| 25 | 30 | 55 | | Scipy's cKDTree (python) | 31 | 47 | 78 | | kiddo (rust)| 26 | 84 | 110 |
With FNNTW's parallel build capability, the build time goes as low as 8.7 ms on the AMD EPYC 7502P. Since the overhead of the parallelism and atomic operations slows down the build when the number of datapoints is small, both a parallel build and non_parallel build are available via Tree:new(..) and Tree::new_parallel(..). The latter takes the aforementioned parameter par_split_level, which is the split depth at which the parallelism begins. For our applications of O(1e5) points, we see the biggest improvement for par_split_level = 1 (and we recommend this value for datasets of this size or smaller), but we suspect that the optimal par_split_level will increase with the size of the dataset.