Jakub Łącki

Tobias Rubel, Richard Wen, Laxman Dhulipala et al.

The fastest indexes for Approximate Nearest Neighbor Search today are also the slowest to build: graph-based methods like HNSW and Vamana achieve state-of-the-art query performance but have large construction times due to relying on random-access-heavy beam searches. We introduce PiPNN (Pick-in-Partitions Nearest Neighbors), an ultra-scalable graph construction algorithm that avoids this ``search bottleneck'' that existing graph-based methods suffer from. PiPNN's core innovation is HashPrune, a novel online pruning algorithm which dynamically maintains sparse collections of edges. HashPrune enables PiPNN to partition the dataset into overlapping sub-problems, efficiently perform bulk distance comparisons via dense matrix multiplication kernels, and stream a subset of the edges into HashPrune. HashPrune guarantees bounded memory during index construction which permits PiPNN to build higher quality indices without the use of extra intermediate memory. PiPNN builds state-of-the-art indexes up to 11.6x faster than Vamana (DiskANN) and up to 12.9x faster than HNSW. PiPNN is significantly more scalable than recent algorithms for fast graph construction. PiPNN builds indexes at least 19.1x faster than MIRAGE and 17.3x than FastKCNA while producing indexes that achieve higher query throughput. PiPNN enables us to build, for the first time, high-quality ANN indexes on billion-scale datasets in under 20 minutes using a single multicore machine.

Kishen N Gowda, Willem Fletcher, MohammadHossein Bateni et al.

Hierarchical Agglomerative Clustering (HAC) is a widely-used clustering method based on repeatedly merging the closest pair of clusters, where inter-cluster distances are determined by a linkage function. Unlike many clustering methods, HAC does not optimize a single explicit global objective; clustering quality is therefore primarily evaluated empirically, and the choice of linkage function plays a crucial role in practice. However, popular classical linkages, such as single-linkage, average-linkage and Ward's method show high variability across real-world datasets and do not consistently produce high-quality clusterings in practice. In this paper, we propose \emph{Chamfer-linkage}, a novel linkage function that measures the distance between clusters using the Chamfer distance, a popular notion of distance between point-clouds in machine learning and computer vision. We argue that Chamfer-linkage satisfies desirable concept representation properties that other popular measures struggle to satisfy. Theoretically, we show that Chamfer-linkage HAC can be implemented in $O(n^2)$ time, matching the efficiency of classical linkage functions. Experimentally, we find that Chamfer-linkage consistently yields higher-quality clusterings than classical linkages such as average-linkage and Ward's method across a diverse collection of datasets. Our results establish Chamfer-linkage as a practical drop-in replacement for classical linkage functions, broadening the toolkit for hierarchical clustering in both theory and practice.