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.ITCS.2018.35
URN: urn:nbn:de:0030-drops-83490
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8349/
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Abboud, Amir ; Rubinstein, Aviad

Fast and Deterministic Constant Factor Approximation Algorithms for LCS Imply New Circuit Lower Bounds

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Abstract

The Longest Common Subsequence (LCS) is one of the most basic similarity measures and it captures important applications in bioinformatics and text analysis. Following the SETH-based nearly-quadratic time lower bounds for LCS from recent years, it is a major open problem to understand the complexity of approximate LCS.
In the last ITCS [AB17] drew an interesting connection between this problem and the area of circuit complexity:
they proved that approximation algorithms for LCS in deterministic truly-subquadratic time imply new circuit lower bounds (E^NP does not have non-uniform linear-size Valiant Series Parallel circuits).

In this work, we strengthen this connection between approximate LCS and circuit complexity by applying the Distributed PCP framework of [ARW17].
We obtain a reduction that holds against much larger approximation factors (super-constant versus 1+o(1)), yields a lower bound for a larger class of circuits (linear-size NC^1), and is also easier to analyze.

BibTeX - Entry

@InProceedings{abboud_et_al:LIPIcs:2018:8349,
  author =	{Amir Abboud and Aviad Rubinstein},
  title =	{{Fast and Deterministic Constant Factor Approximation Algorithms for LCS Imply New Circuit Lower Bounds}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{35:1--35:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Anna R. Karlin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8349},
  URN =		{urn:nbn:de:0030-drops-83490},
  doi =		{10.4230/LIPIcs.ITCS.2018.35},
  annote =	{Keywords: Distributed PCP, Longest Common Subsequence, Fine-grained Complexity, Strong Exponential Time Hypothesis}
}

Keywords: Distributed PCP, Longest Common Subsequence, Fine-grained Complexity, Strong Exponential Time Hypothesis
Collection: 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)
Issue Date: 2018
Date of publication: 12.01.2018

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