{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:42ROZZ3R4TPEV7DLO2K2ZIQ3YT","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":"f8ca4d7fbf9f7ed8473ce71cdc76e9c3c62381dce90c3ba194e85a301da6c27d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-06-15T01:41:52Z","title_canon_sha256":"c25d35193ecdf90c37dad718008abf169a45b18b9da9bc4d7c5682d5231d0b90"},"schema_version":"1.0","source":{"id":"1306.3538","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3538","created_at":"2026-05-18T03:20:47Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3538v1","created_at":"2026-05-18T03:20:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3538","created_at":"2026-05-18T03:20:47Z"},{"alias_kind":"pith_short_12","alias_value":"42ROZZ3R4TPE","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"42ROZZ3R4TPEV7DL","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"42ROZZ3R","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:53d5c3b8e573bca8981438f1912bfd63efc397faeec15b0a694283080a1ce6de","target":"graph","created_at":"2026-05-18T03:20:47Z","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":"A metro-line crossing minimization problem is to draw multiple lines on an underlying graph that models stations and rail tracks so that the number of crossings of lines becomes minimum. It has several variations by adding restrictions on how lines are drawn. Among those, there is one with a restriction that line terminals have to be drawn at a verge of a station, and it is known to be NP-hard even when underlying graphs are paths. This paper studies the problem in this setting, and propose new exact algorithms. We first show that a problem to decide if lines can be drawn without crossings is ","authors_text":"Yoshio Okamoto, Yuichi Tatsu, Yushi Uno","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-06-15T01:41:52Z","title":"Exact and fixed-parameter algorithms for metro-line crossing minimization problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3538","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:a5b936fc7ea474095f492d43f091bda934775b7e05fd63ed55c86fe5b0304a23","target":"record","created_at":"2026-05-18T03:20:47Z","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":"f8ca4d7fbf9f7ed8473ce71cdc76e9c3c62381dce90c3ba194e85a301da6c27d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-06-15T01:41:52Z","title_canon_sha256":"c25d35193ecdf90c37dad718008abf169a45b18b9da9bc4d7c5682d5231d0b90"},"schema_version":"1.0","source":{"id":"1306.3538","kind":"arxiv","version":1}},"canonical_sha256":"e6a2ece771e4de4afc6b7695aca21bc4ed32bf03b55de1b67b3c45ccccf26dfc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6a2ece771e4de4afc6b7695aca21bc4ed32bf03b55de1b67b3c45ccccf26dfc","first_computed_at":"2026-05-18T03:20:47.279140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:47.279140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WhNr1/OTu2kXFYrXopSOj0hTu6nnF6MVvc09vPsAQ9g39xJZoR1bAuc9CS/OlC/hO8pSZ9Zke4UlGfQW9GI+DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:47.279855Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3538","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5b936fc7ea474095f492d43f091bda934775b7e05fd63ed55c86fe5b0304a23","sha256:53d5c3b8e573bca8981438f1912bfd63efc397faeec15b0a694283080a1ce6de"],"state_sha256":"75eac6cfaa7b0affac0fc52d6d70cea15f5f1fda12447b065a3b7ef9fdf56904"}