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DOI: 10.4230/LIPIcs.WABI.2025.17

An Efficient Data Structure and Algorithm for Long-Match Query in Run-Length Compressed BWT

Authors: Ahsan Sanaullah, Degui Zhi, and Shaojie Zhang

Published in: LIPIcs, Volume 344, 25th International Conference on Algorithms for Bioinformatics (WABI 2025)

Abstract

String matching problems in bioinformatics are typically for finding exact substring matches between a query and a reference text. Previous formulations often focus on maximum exact matches (MEMs). However, multiple occurrences of substrings of the query in the text that are long enough but not maximal may not be captured by MEMs. Such long matches can be informative, especially when the text is a collection of similar sequences such as genomes. In this paper, we describe a new type of match between a pattern and a text that aren't necessarily maximal in the query, but still contain useful matching information: locally maximal exact matches (LEMs). There are usually a large amount of LEMs, so we only consider those above some length threshold ℒ. These are referred to as long LEMs. The purpose of long LEMs is to capture substring matches between a query and a text that are not necessarily maximal in the pattern but still long enough to be important. Therefore efficient long LEMs finding algorithms are desired for these datasets. However, these datasets are too large to query on traditional string indexes. Fortunately, these datasets are very repetitive. Recently, compressed string indexes that take advantage of the redundancy in the data but retain efficient querying capability have been proposed as a solution. We therefore give an efficient algorithm for computing all the long LEMs of a query and a text in a BWT runs compressed string index. We describe an O(m+occ) expected time algorithm that relies on an O(r) words space string index for outputting all long LEMs of a pattern with respect to a text given the matching statistics of the pattern with respect to the text. Here m is the length of the query, occ is the number of long LEMs outputted, and r is the number of runs in the BWT of the text. The O(r) space string index we describe relies on an adaptation of the move data structure by Nishimoto and Tabei. We are able to support LCP[i] queries in constant time given SA[i]. In other words, we answer PLCP[i] queries in constant time. These PLCP queries enable the efficient long LEM query. Long LEMs may provide useful similarity information between a pattern and a text that MEMs may ignore. This information is particularly useful in pangenome and biobank scale haplotype panel contexts.

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Ahsan Sanaullah, Degui Zhi, and Shaojie Zhang. An Efficient Data Structure and Algorithm for Long-Match Query in Run-Length Compressed BWT. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 17:1-17:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sanaullah_et_al:LIPIcs.WABI.2025.17,
  author =	{Sanaullah, Ahsan and Zhi, Degui and Zhang, Shaojie},
  title =	{{An Efficient Data Structure and Algorithm for Long-Match Query in Run-Length Compressed BWT}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{17:1--17:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-386-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{344},
  editor =	{Brejov\'{a}, Bro\v{n}a and Patro, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2025.17},
  URN =		{urn:nbn:de:0030-drops-239433},
  doi =		{10.4230/LIPIcs.WABI.2025.17},
  annote =	{Keywords: BWT, LEM, Long LEM, MEM, Run Length Compressed BWT, Move Data Structure, Pangenome}
}

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DOI: 10.4230/LIPIcs.WABI.2022.4

Haplotype Threading Using the Positional Burrows-Wheeler Transform

Authors: Ahsan Sanaullah, Degui Zhi, and Shaoije Zhang

Published in: LIPIcs, Volume 242, 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)

Abstract

In the classic model of population genetics, one haplotype (query) is considered as a mosaic copy of segments from a number of haplotypes in a panel, or threading the haplotype through the panel. The Li and Stephens model parameterized this problem using a hidden Markov model (HMM). However, HMM algorithms are linear to the sample size, and can be very expensive for biobank-scale panels. Here, we formulate the haplotype threading problem as the Minimal Positional Substring Cover problem, where a query is represented by a mosaic of a minimal number of substring matches from the panel. We show that this problem can be solved by a sequential set of greedy set maximal matches. Moreover, the solution space can be bounded by the left-most and the right-most solutions by the greedy approach. Based on these results, we formulate and solve several variations of this problem. Although our results are yet to be generalized to the cases with mismatches, they offer a theoretical framework for designing methods for genotype imputation and haplotype phasing.

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Ahsan Sanaullah, Degui Zhi, and Shaoije Zhang. Haplotype Threading Using the Positional Burrows-Wheeler Transform. In 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 242, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{sanaullah_et_al:LIPIcs.WABI.2022.4,
  author =	{Sanaullah, Ahsan and Zhi, Degui and Zhang, Shaoije},
  title =	{{Haplotype Threading Using the Positional Burrows-Wheeler Transform}},
  booktitle =	{22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)},
  pages =	{4:1--4:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-243-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{242},
  editor =	{Boucher, Christina and Rahmann, Sven},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2022.4},
  URN =		{urn:nbn:de:0030-drops-170386},
  doi =		{10.4230/LIPIcs.WABI.2022.4},
  annote =	{Keywords: Substring Cover, PBWT, Haplotype Threading, Haplotype Matching}
}

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Documents authored by Sanaullah, Ahsan

An Efficient Data Structure and Algorithm for Long-Match Query in Run-Length Compressed BWT

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Haplotype Threading Using the Positional Burrows-Wheeler Transform

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