2026-07-23T08:46:04Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12150 2024-03-06T10:49:25Z ddc:004 open_access

Chaining with Overlaps Revisited Mäkinen, Veli Sahlin, Kristoffer Sparse Dynamic Programming Chaining Maximal Exact Matches Longest Common Subsequence Chaining algorithms aim to form a semi-global alignment of two sequences based on a set of anchoring local alignments as input. Depending on the optimization criteria and the exact definition of a chain, there are several O(n log n) time algorithms to solve this problem optimally, where n is the number of input anchors. In this paper, we focus on a formulation allowing the anchors to overlap in a chain. This formulation was studied by Shibuya and Kurochkin (WABI 2003), but their algorithm comes with no proof of correctness. We revisit and modify their algorithm to consider a strict definition of precedence relation on anchors, adding the required derivation to convince on the correctness of the resulting algorithm that runs in O(n log² n) time on anchors formed by exact matches. With the more relaxed definition of precedence relation considered by Shibuya and Kurochkin or when anchors are non-nested such as matches of uniform length (k-mers), the algorithm takes O(n log n) time. We also establish a connection between chaining with overlaps and the widely studied longest common subsequence problem. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Veli Mäkinen and Kristoffer Sahlin 2020 Is Part Of LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CPM.2020.25 urn:nbn:de:0030-drops-121500 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.25 eng https://creativecommons.org/licenses/by/3.0/legalcode