{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IGZP7SSXIP3ILBN53Q2X74UDEX","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":"a3dafe0338cf2a1a90ed9dec7cb17ee39e6ad88455bb999376202d3a37003a68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-04-26T22:05:27Z","title_canon_sha256":"8c95a917c1ceaad2574a556b529b5462e05778ad6b044e32cbcab6c9db14d4df"},"schema_version":"1.0","source":{"id":"1104.5039","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5039","created_at":"2026-05-18T01:09:50Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5039v2","created_at":"2026-05-18T01:09:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5039","created_at":"2026-05-18T01:09:50Z"},{"alias_kind":"pith_short_12","alias_value":"IGZP7SSXIP3I","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"IGZP7SSXIP3ILBN5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"IGZP7SSX","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:65d61a2a96296a650304eca46d4617edb1060902d7a9220af058c446e4228887","target":"graph","created_at":"2026-05-18T01:09:50Z","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":"Let G be a planar graph and F a set of additional edges not yet in G. The multiple edge insertion problem (MEI) asks for a drawing of G+F with the minimum number of pairwise edge crossings, such that the subdrawing of G is plane. Finding an exact solution to MEI is NP-hard for general F. We present the first polynomial time algorithm for MEI that achieves an additive approximation guarantee -- depending only on the size of F and the maximum degree of G, in the case of connected G. Our algorithm seems to be the first directly implementable one in that realm, too, next to the single edge inserti","authors_text":"Markus Chimani, Petr Hlineny","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-04-26T22:05:27Z","title":"A Tighter Insertion-based Approximation of the Crossing Number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5039","kind":"arxiv","version":2},"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":"sha256:577f8b3fa8b728c815ddc5879ae317542ea3dce6e481e243013dd39590925991","target":"record","created_at":"2026-05-18T01:09:50Z","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":"a3dafe0338cf2a1a90ed9dec7cb17ee39e6ad88455bb999376202d3a37003a68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-04-26T22:05:27Z","title_canon_sha256":"8c95a917c1ceaad2574a556b529b5462e05778ad6b044e32cbcab6c9db14d4df"},"schema_version":"1.0","source":{"id":"1104.5039","kind":"arxiv","version":2}},"canonical_sha256":"41b2ffca5743f68585bddc357ff28325ecae2932fbe67b451c9bc631c74cf500","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41b2ffca5743f68585bddc357ff28325ecae2932fbe67b451c9bc631c74cf500","first_computed_at":"2026-05-18T01:09:50.104442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:50.104442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rMvGk4PoeMQ5z3ty9CPqVtBBDZ82DHPpzsKb8JGNKQFiXByR4G95E8asFA1v7DQCpgCEgX/Ua1Wn0tA+tRUVAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:50.105158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.5039","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:577f8b3fa8b728c815ddc5879ae317542ea3dce6e481e243013dd39590925991","sha256:65d61a2a96296a650304eca46d4617edb1060902d7a9220af058c446e4228887"],"state_sha256":"f87a4a6b6afe2d0e950e3138446e31fce87a5c4875d8679c0e29736285318ec5"}