Efficient k-mer Dataset Compression Using Eulerian Covers of de Bruijn Graphs and BWT

TL;DR

This paper introduces MCTR, a lossless compression algorithm for k-mer datasets using Eulerian covers of de Bruijn graphs and BWT, achieving linear complexity and complete data reconstruction, with performance validated on genomic data.

Contribution

MCTR is the first to combine Eulerian graph covers with BWT for lossless k-mer dataset compression, providing a theoretically grounded, efficient method with proven linear time and space complexity.

Findings

MCTR guarantees lossless reconstruction of k-mer multisets.

MCTR achieves moderate compression ratios on real genomic data.

Full MCTR+BWT pipeline outperforms BWT alone in lossless compression.

Abstract

Transforming an input sequence into its constituent k-mers is a fundamental operation in computational genomics. To reduce storage costs associated with k-mer datasets, we introduce and formally analyze MCTR, a novel two-stage algorithm for lossless compression of the k-mer multiset. Our core method achieves a minimal text representation (W) by computing an optimal Eulerian cover (minimum string count) of the dataset's de Bruijn graph, enabled by an efficient local Eulerization technique. The resulting strings are then further compressed losslessly using the Burrows-Wheeler Transform (BWT). Leveraging de Bruijn graph properties, MCTR is proven to achieve linear time and space complexity and guarantees complete reconstruction of the original k-mer multiset, including frequencies. Using simulated and real genomic data, we evaluated MCTR's performance (list and frequency representations) against the state-of-the-art lossy unitigging tool greedytigs (from matchtigs). We measured core execution time and the raw compression ratio cmpr = weight(M)/weight(W), where M is the input sequence data). Benchmarks confirmed MCTR's data fidelity but revealed performance trade-offs inherent to lossless representation. GreedyTigs was significantly faster. Regarding raw compression, GreedyTigs achieved high ratios (cmpr approx 14) on noisy real data for its lossy sequence output. On real data, MCTR (frequency) showed moderate raw compression (cmpr approx 1.5-2.7), while MCTR (list) showed none (cmpr approx 1). Importantly, the full MCTR+BWT pipeline significantly outperforms BWT alone for enhanced lossless compression. Our results establish MCTR as a valuable, theoretically grounded tool for applications demanding efficient, lossless storage and analysis of k-mer multisets, complementing lossy methods optimized for sequence summarization.