License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.7
URN: urn:nbn:de:0030-drops-140768
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14076/
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Abboud, Amir ; Vassilevska Williams, Virginia

Fine-Grained Hardness for Edit Distance to a Fixed Sequence

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LIPIcs-ICALP-2021-7.pdf (0.7 MB)

Abstract

Nearly all quadratic lower bounds conditioned on the Strong Exponential Time Hypothesis (SETH) start by reducing k-SAT to the Orthogonal Vectors (OV) problem: Given two sets A,B of n binary vectors, decide if there is an orthogonal pair a ∈ A, b ∈ B. In this paper, we give an alternative reduction in which the set A does not depend on the input to k-SAT; thus, the quadratic lower bound for OV holds even if one of the sets is fixed in advance.
Using the reductions in the literature from OV to other problems such as computing similarity measures on strings, we get hardness results of a stronger kind: there is a family of sequences {S_n}_{n = 1}^{∞}, |S_n| = n such that computing the Edit Distance between an input sequence X of length n and the (fixed) sequence S_n requires n^{2-o(1)} time under SETH.

BibTeX - Entry

@InProceedings{abboud_et_al:LIPIcs.ICALP.2021.7,
  author =	{Abboud, Amir and Vassilevska Williams, Virginia},
  title =	{{Fine-Grained Hardness for Edit Distance to a Fixed Sequence}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{7:1--7:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14076},
  URN =		{urn:nbn:de:0030-drops-140768},
  doi =		{10.4230/LIPIcs.ICALP.2021.7},
  annote =	{Keywords: SAT, edit distance, fine-grained complexity, conditional lower bound, sequence alignment}
}

Keywords: SAT, edit distance, fine-grained complexity, conditional lower bound, sequence alignment
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021

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