Parallel Nearest Neighbors in Low Dimensions with Batch Updates

Previous chapter Next chapter Full AccessProceedings 2022 Proceedings of the Symposium on Algorithm Engineering and Experiments (ALENEX)Parallel Nearest Neighbors in Low Dimensions with Batch UpdatesGuy E. Blelloch and Magdalen DobsonGuy E. Blelloch and Magdalen Dobsonpp.195 - 208Chapter DOI:https://doi.org/10.1137/1.9781611977042.16PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract We present a set of parallel algorithms for computing exact k-nearest neighbors in low dimensions. Many k-nearest neighbor algorithms use either a kd-tree or the Morton ordering of the point set; our algorithms combine these approaches using a data structure we call the zd-tree. We show that this combination is both theoretically efficient under common assumptions, and fast in practice. For point sets of size n with bounded expansion constant and bounded ratio, the zd-tree can be built in O(n) work with O(nε) span for constant ε < 1, and searching for the k-nearest neighbors of a point takes expected O(k log k) time. We benchmark our k-nearest neighbor algorithms against existing parallel k-nearest neighbor algorithms, showing that our implementations are generally faster than the state of the art as well as achieving 75x speedup on 144 hyperthreads. Furthermore, the zd-tree supports parallel batch-dynamic insertions and deletions; to our knowledge, it is the first k-nearest neighbor data structure to support such updates. On point sets with bounded expansion constant and bounded ratio, a batch-dynamic update of size k requires O(k log n/k) work with O(kε + polylog(n)) span. Previous chapter Next chapter RelatedDetails Published:2022eISBN:978-1-61197-704-2 https://doi.org/10.1137/1.9781611977042Book Series Name:ProceedingsBook Code:PRAL22Book Pages:iii-220