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DOI: 10.4230/LIPIcs.FSTTCS.2021.11
URN: urn:nbn:de:0030-drops-155228
URL: https://drops.dagstuhl.de/opus/volltexte/2021/15522/
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 | |
| Seminar: | 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 29.11.2021 |
