{"paper":{"title":"Approximate Trace Reconstruction via Median String (in Average-Case)","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Debarati Das, Diptarka Chakraborty, Robert Krauthgamer","submitted_at":"2021-07-20T13:44:54Z","abstract_excerpt":"We consider an \\emph{approximate} version of the trace reconstruction problem, where the goal is to recover an unknown string $s\\in\\{0,1\\}^n$ 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 \\emph{three} traces. It runs in near-linear time $\\tilde O(n)$ and with high probability reports a string within edit distance $O(\\epsilon p n)$ from $s$ for $\\epsilon=\\tilde O(p)$, which significantly i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.09497","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2107.09497/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}