{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QMQO6KWOXV4Y7N2LGX6CFSXLJC","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":"4d68cdcc3a6a549bc79170b243a851d49b6a189fda6f193461ff1858ff47ccd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-05-12T14:22:53Z","title_canon_sha256":"908f66dfb73f7c27d859659de6821c7a1bcb1e32822abfdcf0c4f0bd6a18fdf2"},"schema_version":"1.0","source":{"id":"1705.04587","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04587","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04587v1","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04587","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"pith_short_12","alias_value":"QMQO6KWOXV4Y","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QMQO6KWOXV4Y7N2L","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QMQO6KWO","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:822b149f52359db81d62db90f2bc944958d92701213777c898ea9d58ad4502d2","target":"graph","created_at":"2026-05-18T00:44:37Z","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 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 $\\frac{4}{3} + \\varepsilon$, ","authors_text":"Klaus Jansen, Lars Schmarje, Malin Rau, S\\\"oren Henning","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-05-12T14:22:53Z","title":"Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04587","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":"sha256:5bd087dfc476390a34ba39be0371fae2f47cbb4a0db8713d1fad1437c779c0ed","target":"record","created_at":"2026-05-18T00:44:37Z","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":"4d68cdcc3a6a549bc79170b243a851d49b6a189fda6f193461ff1858ff47ccd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-05-12T14:22:53Z","title_canon_sha256":"908f66dfb73f7c27d859659de6821c7a1bcb1e32822abfdcf0c4f0bd6a18fdf2"},"schema_version":"1.0","source":{"id":"1705.04587","kind":"arxiv","version":1}},"canonical_sha256":"8320ef2acebd798fb74b35fc22caeb489fca6cfb11bb1b7cb41c7b07db8dda37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8320ef2acebd798fb74b35fc22caeb489fca6cfb11bb1b7cb41c7b07db8dda37","first_computed_at":"2026-05-18T00:44:37.721110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:37.721110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rchELIWwNxmHHozy8TCBDPV8sbKmno+E0nqSB9bx2XNTjdduZfXOvF/hFtj1mlaDhV/N+0KDc0gjF3MA0ylZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:37.721676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04587","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bd087dfc476390a34ba39be0371fae2f47cbb4a0db8713d1fad1437c779c0ed","sha256:822b149f52359db81d62db90f2bc944958d92701213777c898ea9d58ad4502d2"],"state_sha256":"0889b37ba6a6f51c0572975454f59f2c68257fc2723e1ed0e6470d2122db1806"}