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• W3184552916 abstract "Previous chapter Next chapter Full AccessProceedings Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Near-Optimal Average-Case Approximate Trace Reconstruction from Few TracesXi Chen, Anindya De, Chin Ho Lee, Rocco A. Servedio, and Sandip SinhaXi Chen, Anindya De, Chin Ho Lee, Rocco A. Servedio, and Sandip Sinhapp.779 - 821Chapter DOI:https://doi.org/10.1137/1.9781611977073.34PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract In the standard trace reconstruction problem, the goal is to exactly reconstruct an unknown source string x ∊ {0, 1}n from independent “traces”, which are copies of x that have been corrupted by a δ-deletion channel which independently deletes each bit of x with probability δ and concatenates the surviving bits. We study the approximate trace reconstruction problem, in which the goal is only to obtain a high-accuracy approximation of x rather than an exact reconstruction. We give an efficient algorithm, and a near-matching lower bound, for approximate reconstruction of a random source string x ∊ {0, 1}n from few traces. Our main algorithmic result is a polynomial-time algorithm with the following property: for any deletion rate 0 < δ < 1 (which may depend on n), for almost every source string x ∊ {0,1}n, given any number M ≤ Θ(1/δ) of traces from Delδ(x), the algorithm constructs a hypothesis string that has edit distance at most n · (δM)Ω(M) from x. We also prove a near-matching information-theoretic lower bound showing that given M ≤ Θ(1/δ) traces from Delδ(x) for a random n-bit string x, the smallest possible expected edit distance that any algorithm can achieve, regardless of its running time, is n · (δM)O(M). Previous chapter Next chapter RelatedDetails Published:2022eISBN:978-1-61197-707-3 https://doi.org/10.1137/1.9781611977073Book Series Name:ProceedingsBook Code:PRDA22Book Pages:xvii + 3771" @default.
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• W3184552916 date "2022-01-01" @default.
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• W3184552916 title "Near-Optimal Average-Case Approximate Trace Reconstruction from Few Traces" @default.
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• W3184552916 doi "https://doi.org/10.1137/1.9781611977073.34" @default.
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