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Chaining with Overlaps Revisited

Authors Veli Mäkinen , Kristoffer Sahlin

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Veli Mäkinen
  • Department of Computer Science, University of Helsinki, Finland
Kristoffer Sahlin
  • Department of Mathematics, Science for Life Laboratory, Stockholm University, Sweden


We wish to thank Manuel Cáceres for spotting a mistake in our original coverage definition regarding nested anchors and the anonymous reviewers for useful suggestions to improve the readability.

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Veli Mäkinen and Kristoffer Sahlin. Chaining with Overlaps Revisited. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 25:1-25:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
  • Theory of computation → Dynamic programming
  • Applied computing → Genomics
  • Sparse Dynamic Programming
  • Chaining
  • Maximal Exact Matches
  • Longest Common Subsequence


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