Scaling the PBWT for Long-Range Shared Ancestry Detection in Large Haplotype Panels

Detecting long shared ancestry tracts in large haplotype panels is central to IBD analysis, imputation, and local ancestry inference, and can be approximated computationally by finding Set-Maximal Exact Matches (SMEMs) between sequences. The Positional Burrows-Wheeler Transform (PBWT) provides an efficient index for these panels, yet current methods often enumerate all SMEMs, producing a large number of short, uninformative matches. We introduce Positional Boyer- Moore-Li (PBML), which restricts enumeration to SMEMs occurring in at least k haplotypes and spanning at least L sites (kL-SMEMs). PBML is the first algorithm for computing KL-SMEMs on top of a single compressed run-length encoded PBWT index reusable for any (k, L) without rebuilding. On the 1000 Genomes Project, PBML achieves 4.6x faster query time than {micro}-PBWT and 2.4x over Durbins PBWT with lower memory, scaling to 15.9x over {micro}-PBWT at 16 threads. On a 10,000-haplotype panel from the Tennessee BIG Initiative, a diverse admixed cohort, PBML outperforms {micro}-PBWT by up to 4.7x in k-SMEM finding. By applying both thresholds during traversal, PBML extracts biologically informative, population-shared segments while filtering millions of short matches, a capability not available in current tools. On the BIG panel, in about 10 seconds PBML finds 2,441 long tracts at (k = 50, L = 5000) shared by an average of 60 haplotypes against 1000 queries, significantly reducing the 4.8 million unfiltered SMEMs shared on average by 2 haplotypes. These results establish PBML as a scalable tool for targeted long-range shared ancestry detection in large, diverse panels.