{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5SXFJOHZTRMLLFHKLQB6YQ6Q34","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e5703a0823fad304318fdaad9f8cb5bbc4cf92d133fa64280fdf04f964ea6b35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-02-09T14:25:23Z","title_canon_sha256":"e8c69ac04eff375c412b416f161541ce5af3565782647b0721d88f7f352eb30d"},"schema_version":"1.0","source":{"id":"1902.03428","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03428","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03428v1","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03428","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"5SXFJOHZTRML","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5SXFJOHZTRMLLFHK","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5SXFJOHZ","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:04633defab9ac36950f663ad62f5ac1057ce5f67e51c09a64cafa826de7f2fca","target":"graph","created_at":"2026-05-17T23:54:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the Multiple Cluster Scheduling problem and the Multiple Strip Packing problem. For both problems, there is no algorithm with approximation ratio better than $2$ unless $P = NP$. In this paper, we present an algorithm with approximation ratio $2$ and running time $O(n)$ for both problems. While a $2$ approximation was known before, the running time of the algorithm is at least $\\Omega(n^{256})$ in the worst case. Therefore, an $O(n)$ algorithm is surprising and the best possible. We archive this result by calling an AEPTAS with approximation guarantee $(1+\\varepsilon)OPT +p_{\\max}$ an","authors_text":"Klaus Jansen, Malin Rau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-02-09T14:25:23Z","title":"Linear Time Algorithms for Multiple Cluster Scheduling and Multiple Strip Packing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03428","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:da508f85943a2db345c861db726ae7467daa426d12f6dc8d616e40596c6e693b","target":"record","created_at":"2026-05-17T23:54:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e5703a0823fad304318fdaad9f8cb5bbc4cf92d133fa64280fdf04f964ea6b35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-02-09T14:25:23Z","title_canon_sha256":"e8c69ac04eff375c412b416f161541ce5af3565782647b0721d88f7f352eb30d"},"schema_version":"1.0","source":{"id":"1902.03428","kind":"arxiv","version":1}},"canonical_sha256":"ecae54b8f99c58b594ea5c03ec43d0df0a4822a99fdf58f6115a855999988b0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecae54b8f99c58b594ea5c03ec43d0df0a4822a99fdf58f6115a855999988b0b","first_computed_at":"2026-05-17T23:54:20.871102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:20.871102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"twfdcZlP5ihFmtPsSKmnLKWjdB9LLIrdTtZk8f4JTMDQ2eAXFueKjWlmxY69CEJOrRARGJB9uJp/Q4Kx+ZxUCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:20.872540Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03428","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da508f85943a2db345c861db726ae7467daa426d12f6dc8d616e40596c6e693b","sha256:04633defab9ac36950f663ad62f5ac1057ce5f67e51c09a64cafa826de7f2fca"],"state_sha256":"c9ac649a564cc7f3862cff9d00ffe037412fa896ee9c64dad1a4aaa96bdd35a1"}