{"paper":{"title":"Truly Sub-cubic Algorithms for Language Edit Distance and RNA Folding via Fast Bounded-Difference Min-Plus Product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Barna Saha, Fabrizio Grandoni, Karl Bringmann, Virginia Vassilevska Williams","submitted_at":"2017-07-17T11:13:16Z","abstract_excerpt":"It is a major open problem whether the $(\\min,+)$-product of two $n\\times n$ matrices has a truly sub-cubic (i.e. $O(n^{3-\\epsilon})$ for $\\epsilon>0$) time algorithm, in particular since it is equivalent to the famous All-Pairs-Shortest-Paths problem (APSP) in $n$-vertex graphs. Some restrictions of the $(\\min,+)$-product to special types of matrices are known to admit truly sub-cubic algorithms, each giving rise to a special case of APSP that can be solved faster. In this paper we consider a new, different and powerful restriction in which all matrix entries are integers and one matrix can b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05095","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"}