HyperSketch: de Bruijn graph sketching for genomic similarity estimation with Hyperdimensional Computing

The exponential growth of genomic databases necessitates alignment-free methods for comparing genomes. While MinHash-based tools have revolutionized this field by efficiently estimating the Average Nucleotide Identity based on k-mer sets, they inherently discard structural genomic information. We introduce HyperSketch, a novel sketching tool that encodes the de Bruijn graph structure of a genome into a fixed-size, topology-aware vector using Hyperdimensional Computing (HDC). Unlike set-based sketches, HyperSketch encodes the transitions between adjacent k-mers into a superposition of orthogonal hypervectors. To formalize parameter selection, we also propose an analytical framework proving that graph-based sketches fundamentally require a smaller k-mer size than set-based models due to their expanded k+1 biological footprint. We benchmarked HyperSketch against Mash and HyperGen using a dataset of ~26 thousand viral reference genomes from NCBI GenBank. Under optimal parameters, we demonstrate a strong linear correlation (>99%) between the graph-based similarity computed by HyperSketch and standard MinHash distance estimates. Crucially, we show that the mathematical formulation of HyperSketch introduces a distance scaling effect that expands the dynamic range of estimates for closely related strains, providing a higher-resolution metric for sub-lineage clustering than purely compositional estimators. HyperSketch provides a computationally efficient, structure-aware alternative to traditional sketching. By natively encoding genomic syntax, it offers a new dimension of genomic comparison that excels at both high-resolution strain differentiation and deep evolutionary scaling, complementing existing nucleotide identity metrics without requiring sequence alignment.