# Hilbert Forest in the SISAP 2025 Indexing Challenge

## TL;DR

This paper introduces the Hilbert forest, a novel high-dimensional indexing method using Hilbert space-filling curves, demonstrating competitive and efficient approximate nearest neighbor search and graph construction under resource constraints.

## Contribution

The paper presents the Hilbert forest, a new indexing technique leveraging Hilbert curves for efficient high-dimensional data retrieval, especially under limited memory conditions.

## Key findings

- Competitive performance in approximate search
- Fastest construction time for k-NN graph
- Effective under strict memory constraints

## Abstract

We report our participation in the SISAP 2025 Indexing Challenge using a novel indexing technique called the Hilbert forest. The method is based on the fast Hilbert sort algorithm, which efficiently orders high-dimensional points along a Hilbert space-filling curve, and constructs multiple Hilbert trees to support approximate nearest neighbor search. We submitted implementations to both Task 1 (approximate search on the PUBMED23 dataset) and Task 2 (k-nearest neighbor graph construction on the GOOAQ dataset) under the official resource constraints of 16 GB RAM and 8 CPU cores. The Hilbert forest demonstrated competitive performance in Task 1 and achieved the fastest construction time in Task 2 while satisfying the required recall levels. These results highlight the practical effectiveness of Hilbert order-based indexing under strict memory limitations.