License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/LIPIcs.FSTTCS.2021.11
URN: urn:nbn:de:0030-drops-155228
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15522/
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Chakraborty, Diptarka ; Das, Debarati ; Krauthgamer, Robert

Approximate Trace Reconstruction via Median String (In Average-Case)

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Abstract

We consider an approximate version of the trace reconstruction problem, where the goal is to recover an unknown string s ∈ {0,1}ⁿ from m traces (each trace is generated independently by passing s through a probabilistic insertion-deletion channel with rate p). We present a deterministic near-linear time algorithm for the average-case model, where s is random, that uses only three traces. It runs in near-linear time Õ(n) and with high probability reports a string within edit distance Õ(p² n) from s, which significantly improves over the straightforward bound of O(pn).
Technically, our algorithm computes a (1+ε)-approximate median of the three input traces. To prove its correctness, our probabilistic analysis shows that an approximate median is indeed close to the unknown s. To achieve a near-linear time bound, we have to bypass the well-known dynamic programming algorithm that computes an optimal median in time O(n³).

BibTeX - Entry

@InProceedings{chakraborty_et_al:LIPIcs.FSTTCS.2021.11,
  author =	{Chakraborty, Diptarka and Das, Debarati and Krauthgamer, Robert},
  title =	{{Approximate Trace Reconstruction via Median String (In Average-Case)}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{11:1--11:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czy, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15522},
  URN =		{urn:nbn:de:0030-drops-155228},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.11},
  annote =	{Keywords: Trace Reconstruction, Approximation Algorithms, Edit Distance, String Median}
}

Keywords: Trace Reconstruction, Approximation Algorithms, Edit Distance, String Median
Collection: 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)
Issue Date: 2021
Date of publication: 29.11.2021

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