{"paper":{"title":"Optimal mean-based algorithms for trace reconstruction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG"],"primary_cat":"cs.CC","authors_text":"Anindya De, Rocco Servedio, Ryan O'Donnell","submitted_at":"2016-12-09T20:05:19Z","abstract_excerpt":"In the (deletion-channel) trace reconstruction problem, there is an unknown $n$-bit source string $x$. An algorithm is given access to independent traces of $x$, where a trace is formed by deleting each bit of~$x$ independently with probability~$\\delta$. The goal of the algorithm is to recover~$x$ exactly (with high probability), while minimizing samples (number of traces) and running time.\n  Previously, the best known algorithm for the trace reconstruction problem was due to Holenstein~et~al.; it uses $\\exp(\\tilde{O}(n^{1/2}))$ samples and running time for any fixed $0 < \\delta < 1$. It is al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03148","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":""},"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"}