VLSH: Voronoi-based locality sensitive hashing

Tieu Lin Loi, Jae-Pil Heo, Junghwan Lee, Sung-Eui Yoon

Abstract: We present a fast, yet accurate k-nearest neighbor search algorithm for high-dimensional sampling-based motion planners. Our technique is built on top of Locality Sensitive Hashing (LSH), but is extended to support arbitrary distance metrics used for motion planning problems and adapt irregular distributions of samples generated in the configuration space. To enable such novel characteristics our method embeds samples generated in the configuration space into a simple l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm space by using pivot points. We then implicitly define Voronoi regions and use local LSHs with varying quantization factors for those Voronoi regions. We have applied our method and other prior techniques to high-dimensional motion planning problems. Our method is able to show performance improvement by a factor of up to three times even with higher accuracy over prior, approximate nearest neighbor search techniques.