{"paper":{"title":"Polynomial-Time Approximation Schemes for Circle and Other Packing Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Fl\\'avio K. Miyazawa, Lehilton L. C. Pedrosa, Maxim Sviridenko, Rafael C. S. Schouery, Yoshiko Wakabayashi","submitted_at":"2014-12-15T18:27:32Z","abstract_excerpt":"We give an asymptotic approximation scheme (APTAS) for the problem of packing a set of circles into a minimum number of unit square bins. To obtain rational solutions, we use augmented bins of height $1+\\gamma$, for some arbitrarily small number $\\gamma > 0$. Our algorithm is polynomial on $\\log 1/\\gamma$, and thus $\\gamma$ is part of the problem input. For the special case that $\\gamma$ is constant, we give a (one dimensional) resource augmentation scheme, that is, we obtain a packing into bins of unit width and height $1+\\gamma$ using no more than the number of bins in an optimal packing. Ad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4709","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"}