License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2020.25
URN: urn:nbn:de:0030-drops-121500
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Mäkinen, Veli ; Sahlin, Kristoffer

Chaining with Overlaps Revisited

LIPIcs-CPM-2020-25.pdf (0.5 MB)


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.

BibTeX - Entry

  author =	{Veli M{\"a}kinen and Kristoffer Sahlin},
  title =	{{Chaining with Overlaps Revisited}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{25:1--25:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{Inge Li G{\o}rtz and Oren Weimann},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-121500},
  doi =		{10.4230/LIPIcs.CPM.2020.25},
  annote =	{Keywords: Sparse Dynamic Programming, Chaining, Maximal Exact Matches, Longest Common Subsequence}

Keywords: Sparse Dynamic Programming, Chaining, Maximal Exact Matches, Longest Common Subsequence
Collection: 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)
Issue Date: 2020
Date of publication: 09.06.2020

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