{"paper":{"title":"Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Klaus Jansen, Lars Schmarje, Malin Rau, S\\\"oren Henning","submitted_at":"2017-05-12T14:22:53Z","abstract_excerpt":"We study the Parallel Task Scheduling problem $Pm|size_j|C_{\\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \\geq 5$, while it is solvable in pseudo-polynomial time for each $m \\leq 3$. We give a positive answer to the long-standing open question whether this problem is strongly $NP$-complete for $m=4$. As a second result, we improve the lower bound of $\\frac{12}{11}$ for approximating pseudo-polynomial Strip Packing to $\\frac{5}{4}$. Since the best known approximation algorithm for this problem has a ratio of $\\frac{4}{3} + \\varepsilon$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04587","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"}