# On the Merge of k-NN Graph

## TL;DR

This paper introduces new algorithms for merging and expanding approximate k-NN graphs, enabling scalable and hierarchical construction and search, which improves efficiency in large-scale data processing.

## Contribution

It presents the first algorithms for merging existing k-NN graphs and incrementally expanding them, addressing a previously overlooked problem in the field.

## Key findings

- Efficient symmetric merge algorithm for approximate k-NN graphs
- Hierarchical expansion method improves NN search across data types
- Superior performance demonstrated in large-scale and high-dimensional datasets

## Abstract

k-nearest neighbor graph is a fundamental data structure in many disciplines such as information retrieval, data-mining, pattern recognition, and machine learning, etc. In the literature, considerable research has been focusing on how to efficiently build an approximate k-nearest neighbor graph (k-NN graph) for a fixed dataset. Unfortunately, a closely related issue of how to merge two existing k-NN graphs has been overlooked. In this paper, we address the issue of k-NN graph merging in two different scenarios. In the first scenario, a symmetric merge algorithm is proposed to combine two approximate k-NN graphs. The algorithm facilitates large-scale processing by the efficient merging of k-NN graphs that are produced in parallel. In the second scenario, a joint merge algorithm is proposed to expand an existing k-NN graph with a raw dataset. The algorithm enables the incremental construction of a hierarchical approximate k-NN graph. Superior performance is attained when leveraging the hierarchy for NN search of various data types, dimensionality, and distance measures.