{"paper":{"title":"On problems equivalent to (min,+)-convolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Karol W\\k{e}grzycki, Marcin Mucha, Marek Cygan, Micha{\\l} W{\\l}odarczyk","submitted_at":"2017-02-24T17:18:02Z","abstract_excerpt":"In recent years, significant progress has been made in explaining the apparent hardness of improving upon the naive solutions for many fundamental polynomially solvable problems. This progress has come in the form of conditional lower bounds -- reductions from a problem assumed to be hard. The hard problems include 3SUM, All-Pairs Shortest Path, SAT, Orthogonal Vectors, and others.\n  In the $(\\min,+)$-convolution problem, the goal is to compute a sequence $(c[i])^{n-1}_{i=0}$, where $c[k] = $ $\\min_{i=0,\\ldots,k} $ $\\{a[i] $ $+$ $b[k-i]\\}$, given sequences $(a[i])^{n-1}_{i=0}$ and $(b[i])_{i=0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07669","kind":"arxiv","version":2},"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"}