Chaining with Overlaps Revisited

Authors Veli Mäkinen , Kristoffer Sahlin

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Author Details

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.

Cite AsGet BibTex

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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