{"paper":{"title":"Faster Exponential Algorithms for Multi-Machine Scheduling Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ahmed Ghazy, Anita D\\\"urr, Anubhav Dhar, Jakob Greilhuber, Karol W\\k{e}grzycki","submitted_at":"2026-08-12T16:22:21Z","abstract_excerpt":"Minimizing the weighted completion times ($P \\mid \\mid \\Sigma w_j C_j$) and weighted number of tardy jobs ($P \\mid \\mid \\Sigma w_j U_j$) on multiple identical machines are two classical NP-hard scheduling problems. As shown by Lent\\'e et al. (2014), both problems can be solved in time ${O}^{\\star}(3^n)$. In this paper, we improve these bounds to ${O}(2.755^n)$ and ${O}^{\\star}(2^n)$, respectively. Our algorithm for $P \\mid \\mid \\Sigma w_j C_j$ exploits the meet-in-the-middle paradigm and an efficient data structure answering linear programming queries. Additionally, when the number of machines"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12224","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.12224/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}