{"paper":{"title":"Edit Distance: Sketching, Streaming and Document Exchange","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Djamal Belazzougui, Qin Zhang","submitted_at":"2016-07-14T16:38:17Z","abstract_excerpt":"We show that in the document exchange problem, where Alice holds $x \\in \\{0,1\\}^n$ and Bob holds $y \\in \\{0,1\\}^n$, Alice can send Bob a message of size $O(K(\\log^2 K+\\log n))$ bits such that Bob can recover $x$ using the message and his input $y$ if the edit distance between $x$ and $y$ is no more than $K$, and output \"error\" otherwise. Both the encoding and decoding can be done in time $\\tilde{O}(n+\\mathsf{poly}(K))$. This result significantly improves the previous communication bounds under polynomial encoding/decoding time. We also show that in the referee model, where Alice and Bob hold $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04200","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"}