{"paper":{"title":"How to Store a Random Walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"Emanuele Viola, Huacheng Yu, Omri Weinstein","submitted_at":"2019-07-25T07:37:42Z","abstract_excerpt":"Motivated by storage applications, we study the following data structure problem: An encoder wishes to store a collection of jointly-distributed files $\\overline{X}:=(X_1,X_2,\\ldots, X_n) \\sim \\mu$ which are \\emph{correlated} ($H_\\mu(\\overline{X}) \\ll \\sum_i H_\\mu(X_i)$), using as little (expected) memory as possible, such that each individual file $X_i$ can be recovered quickly with few (ideally constant) memory accesses.\n  In the case of independent random files, a dramatic result by \\Pat (FOCS'08) and subsequently by Dodis, \\Pat and Thorup (STOC'10) shows that it is possible to store $\\over"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10874","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"}