{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ENKQXT5UVDRRRWP5X7WUHWOJFN","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":"5145e9b9c5f76f9eccf3ed22f0c7422cb153c2fdc2276497dbe9833b7c1de5ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-11-02T02:46:56Z","title_canon_sha256":"bc1aa29733e81bf2f06ee9e635bee4ed69c587e600b0ea9d36eea0597275dd89"},"schema_version":"1.0","source":{"id":"1711.00599","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00599","created_at":"2026-05-18T00:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00599v1","created_at":"2026-05-18T00:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00599","created_at":"2026-05-18T00:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"ENKQXT5UVDRR","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ENKQXT5UVDRRRWP5","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ENKQXT5U","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:a799b91362a51cb7dd2f344ef1bee5436879f4fd12ec831cb402a330d7faa9b2","target":"graph","created_at":"2026-05-18T00:31:30Z","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 present linear-time algorithms for partitioning a path or a tree with weights on the vertices by removing $k$ edges to maximize the minimum-weight component. We also use the same framework to partition a path with weight on the vertices, removing $k$ edges to minimize the maximum-weight component. The algorithms use the parametric search paradigm, testing candidate values until an optimum is found while simultaneously reducing the running time needed for each test. For path-partitioning, the algorithm employs a synthetic weighting scheme that results in a constant fraction reduction in runn","authors_text":"Greg N. Frederickson, Samson Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-11-02T02:46:56Z","title":"Optimal Parametric Search for Path and Tree Partitioning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00599","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":"sha256:47ec6d54b53b26ea518d5b67b4cd811740bee64dd54ac6b92ef48aeb1314d077","target":"record","created_at":"2026-05-18T00:31:30Z","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":"5145e9b9c5f76f9eccf3ed22f0c7422cb153c2fdc2276497dbe9833b7c1de5ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-11-02T02:46:56Z","title_canon_sha256":"bc1aa29733e81bf2f06ee9e635bee4ed69c587e600b0ea9d36eea0597275dd89"},"schema_version":"1.0","source":{"id":"1711.00599","kind":"arxiv","version":1}},"canonical_sha256":"23550bcfb4a8e318d9fdbfed43d9c92b6fe8f30ae7b5bba19b373dcc67ae38d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23550bcfb4a8e318d9fdbfed43d9c92b6fe8f30ae7b5bba19b373dcc67ae38d7","first_computed_at":"2026-05-18T00:31:30.065008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:30.065008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"magMagIyd77O5GmYg/yt9AnY3p4tY8sdQKwJfEhIbDrvl4h+Xpt1qJI6HZ7XgXvnD1jEkUk3XKcdFOox1ry3Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:30.065653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.00599","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47ec6d54b53b26ea518d5b67b4cd811740bee64dd54ac6b92ef48aeb1314d077","sha256:a799b91362a51cb7dd2f344ef1bee5436879f4fd12ec831cb402a330d7faa9b2"],"state_sha256":"d6dd881485c365cd62cd66072f8747bc10c5f120452ca0982c4b69a2b0ec2ff4"}