{"paper":{"title":"Closing the Gap for Makespan Scheduling via Sparsification Techniques","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jos\\'e Verschae, Kim-Manuel Klein, Klaus Jansen","submitted_at":"2016-04-25T07:47:34Z","abstract_excerpt":"Makespan scheduling on identical machines is one of the most basic and fundamental packing problems studied in the discrete optimization literature. It asks for an assignment of $n$ jobs to a set of $m$ identical machines that minimizes the makespan. The problem is strongly NP-hard, and thus we do not expect a $(1+\\epsilon)$-approximation algorithm with a running time that depends polynomially on $1/\\epsilon$. Furthermore, Chen et al. [3] recently showed that a running time of $2^{(1/\\epsilon)^{1-\\delta}}+\\text{poly}(n)$ for any $\\delta>0$ would imply that the Exponential Time Hypothesis (ETH)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07153","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"}