# Browsing by Subject "Chaining"

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• (Helsingin yliopisto, 2020)
Computing an edit distance between strings is one of the central problems in both string processing and bioinformatics. Optimal solutions to edit distance are quadratic to the lengths of the input strings. The goal of this thesis is to study a new approach to approximate edit distance. We use a chaining algorithm presented by Mäkinen and Sahlin in "Chaining with overlaps revisited" CPM 2020 implemented verbatim. Building on the chaining algorithm, our focus is on efficiently finding a good set of anchors for the chaining algorithm. We present three approaches to computing the anchors as maximal exact matches: Bi-Directional Burrows-Wheeler Transform, Minimizers, and lastly, a hybrid implementation of the two. Using the maximal exact matches as anchors, we can efficiently compute an optimal chaining alignment for the strings. The chaining alignment further allows us to determine all such intervals where mismatches occur by looking at which sequences are not in the chain. Using these smaller intervals lets us approximate edit distance with a high degree of accuracy and a significant speed improvement. The methods described present a way to approximate edit distance in time complexity bounded by the number of maximal exact matches.
• (Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020)
Leibniz International Proceedings in Informatics, LIPIcs
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. 2012 ACM Subject Classification Theory of computation ! Pattern matching; Theory of computation ! Dynamic programming; Applied computing ! Genomics.