Lossless Approximate Pattern Matching: Automated Design of Efficient Search Schemes

This study introduces a pioneering approach to automate the creation of search schemes for lossless approximate pattern matching. Search schemes are combinatorial structures that define a series of searches over a partitioned pattern. Each search specifies the processing order of these parts and the cumulative lower and upper bounds on the number of errors in each part of the pattern. Together, these searches ensure the identification of all approximate occurrences of a search pattern within a predefined limit of <i>k</i> errors. While existing literature offers designed schemes for up to <i>k</i> = 4 errors, designing search schemes for larger <i>k</i> values incurs escalating computational costs. Our method integrates a greedy algorithm and a novel Integer Linear Programming (ILP) formulation to design efficient search schemes for up to <i>k</i> = 7 errors. Comparative analyses demonstrate the superiority of our ILP-optimal schemes over alternative strategies in both theoretical and practical contexts. Additionally, we propose a dynamic scheme selection technique tailored to specific search patterns, further enhancing efficiency. Combined, this yields runtime reductions of up to 53% for higher <i>k</i> values. To facilitate search scheme generation, we present Hato, an open-source software tool (AGPL-3.0 license) employing the greedy algorithm and utilizing CPLEX for ILP solving. Furthermore, we introduce Columba 1.2, an open-source lossless read-mapper (AGPL-3.0 license) implemented in C++. Columba surpasses existing state-of-the-art tools by identifying all approximate occurrences of 100,000 Illumina reads (150 bp) in the human reference genome within 24 seconds (maximum edit distance of 4) and 75 seconds (maximum edit distance of 6) using a single CPU core. Notably, our study showcases Columba's capability to align 100,000 reads of length 50, with high error rates and up to an edit distance of 7, in a mere 2 hours and 15 minutes. This achievement is unmatched by other lossless aligners, which require over 3 hours for edit distance 5 alignments. Moreover, Columba exhibits a mapping rate four times higher than that of a lossy tool for this dataset.