{"paper":{"title":"Strategies for Stable Merge Sorting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alexander Knop, Sam Buss","submitted_at":"2018-01-15T02:16:39Z","abstract_excerpt":"We introduce new stable natural merge sort algorithms, called $2$-merge sort and $\\alpha$-merge sort. We prove upper and lower bounds for several merge sort algorithms, including Timsort, Shivers' sort, $\\alpha$-stack sorts, and our new $2$-merge and $\\alpha$-merge sorts. The upper and lower bounds have the forms $c \\cdot n \\log m$ and $c \\cdot n \\log n$ for inputs of length~$n$ comprising $m$~monotone runs. For Timsort, we prove a lower bound of $(1.5 - o(1)) n \\log n$. For $2$-merge sort, we prove optimal upper and lower bounds of approximately $(1.089 \\pm o(1))n \\log m$. We prove similar as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04641","kind":"arxiv","version":4},"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"}