{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WDBQP5LNRCZCCIZND6BN5T2JQT","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":"0b0459063b94242e2afd485a89e769f802c8c49cae9a337b802d8d215abde2eb","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.CC","submitted_at":"2025-06-06T14:55:12Z","title_canon_sha256":"6080a3e96b084ed23b345eb550ab225f13ecd73dfc0a098e74999c91d01cb83e"},"schema_version":"1.0","source":{"id":"2506.06138","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.06138","created_at":"2026-07-05T11:17:26Z"},{"alias_kind":"arxiv_version","alias_value":"2506.06138v1","created_at":"2026-07-05T11:17:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.06138","created_at":"2026-07-05T11:17:26Z"},{"alias_kind":"pith_short_12","alias_value":"WDBQP5LNRCZC","created_at":"2026-07-05T11:17:26Z"},{"alias_kind":"pith_short_16","alias_value":"WDBQP5LNRCZCCIZN","created_at":"2026-07-05T11:17:26Z"},{"alias_kind":"pith_short_8","alias_value":"WDBQP5LN","created_at":"2026-07-05T11:17:26Z"}],"graph_snapshots":[{"event_id":"sha256:f08da8f8d471faadbacde25afa15e1baf52f50d3dde5391a07de45d21d009ca6","target":"graph","created_at":"2026-07-05T11:17:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.06138/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Dembo-Hammer's Reduction Algorithm (DHR) is one of the classical algorithms for the 0-1 Knapsack Problem (0-1 KP) and its variants, which reduces an instance of the 0-1 KP to a sub-instance of smaller size with reduction time complexity $O(n)$. We present an extension of DHR (abbreviated as EDHR), which reduces an instance of 0-1 KP to at most $n^i$ sub-instances for any positive integer $i$. In practice, $i$ can be set as needed. In particular, if we choose $i=1$ then EDHR is exactly DHR. Finally, computational experiments on randomly generated data instances demonstrate that EDHR substantial","authors_text":"Yang Yang","cross_cats":["cs.DS"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.CC","submitted_at":"2025-06-06T14:55:12Z","title":"An extension of Dembo-Hammer's reduction algorithm for the 0-1 knapsack problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.06138","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:f29d157d3fe54c4680b5d5e99987ff2b5e2ea4530dccab67395a826eaeec5584","target":"record","created_at":"2026-07-05T11:17:26Z","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":"0b0459063b94242e2afd485a89e769f802c8c49cae9a337b802d8d215abde2eb","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.CC","submitted_at":"2025-06-06T14:55:12Z","title_canon_sha256":"6080a3e96b084ed23b345eb550ab225f13ecd73dfc0a098e74999c91d01cb83e"},"schema_version":"1.0","source":{"id":"2506.06138","kind":"arxiv","version":1}},"canonical_sha256":"b0c307f56d88b221232d1f82decf4984e339ac7f271be6928f9f83bef994f954","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0c307f56d88b221232d1f82decf4984e339ac7f271be6928f9f83bef994f954","first_computed_at":"2026-07-05T11:17:26.389208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:17:26.389208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DQW2K+bdwxTuhMcOvwDgF39+kBnC7/u54YOn/F8DJSRdM5eJVbQ2ALaGjlgAFmJZRBWZLcNz8VJSH8vfPjLrDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:17:26.389722Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.06138","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f29d157d3fe54c4680b5d5e99987ff2b5e2ea4530dccab67395a826eaeec5584","sha256:f08da8f8d471faadbacde25afa15e1baf52f50d3dde5391a07de45d21d009ca6"],"state_sha256":"d5ba461c3f06f630fc6c81e3634187e7d586d5db8415805befcfaf5536788731"}