Hairpin Completion Distance Lower Bound

Authors Itai Boneh , Dvir Fried , Shay Golan , Matan Kraus



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Author Details

Itai Boneh
  • Reichman University and University of Haifa, Israel
Dvir Fried
  • Bar Ilan University, Ramat Gan, Israel
Shay Golan
  • Reichman University and University of Haifa, Israel
Matan Kraus
  • Bar Ilan University, Ramat Gan, Israel

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Itai Boneh, Dvir Fried, Shay Golan, and Matan Kraus. Hairpin Completion Distance Lower Bound. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CPM.2024.11

Abstract

Hairpin completion, derived from the hairpin formation observed in DNA biochemistry, is an operation applied to strings, particularly useful in DNA computing. Conceptually, a right hairpin completion operation transforms a string S into S⋅ S' where S' is the reverse complement of a prefix of S. Similarly, a left hairpin completion operation transforms a string S into S'⋅ S where S' is the reverse complement of a suffix of S. The hairpin completion distance from S to T is the minimum number of hairpin completion operations needed to transform S into T. Recently Boneh et al. [Itai Boneh et al., 2023] showed an O(n²) time algorithm for finding the hairpin completion distance between two strings of length at most n. In this paper we show that for any ε > 0 there is no O(n^{2-ε})-time algorithm for the hairpin completion distance problem unless the Strong Exponential Time Hypothesis (SETH) is false. Thus, under SETH, the time complexity of the hairpin completion distance problem is quadratic, up to sub-polynomial factors.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Fine-grained complexity
  • Hairpin completion
  • LCS

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