{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ACAFODMEKQAM6M6JWHWO3NMWQO","short_pith_number":"pith:ACAFODME","schema_version":"1.0","canonical_sha256":"0080570d845400cf33c9b1ecedb596839d52666a932bc2cc2cf72c831286447c","source":{"kind":"arxiv","id":"1112.6079","version":2},"attestation_state":"computed","paper":{"title":"Determining the Solution Space of Vertex-Cover by Interactions and Backbones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Binghui Guo, Renquan Zhang, Wei Wei, Zhiming Zheng","submitted_at":"2011-12-28T08:32:37Z","abstract_excerpt":"To solve the combinatorial optimization problems especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of Vertex-cover, a new structure named interaction between nodes is defined and discovered for random graph, which results in the emergence of the frustration and long-range correlation phenomenon. Based on the backbones and interactions with a node adding process, we propose an Interaction and Backbone Evolution Algorithm to achieve the reduced solution graph, whi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1112.6079","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-28T08:32:37Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"45ab5784abb0a1d8aeb5d17ade997fe55165326b9a978c472f2f7f07aa3dd1ed","abstract_canon_sha256":"0f8bfc240d4eeb898323dee9f787e975a516517df9ea92db77f9b061eae272d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:09.189026Z","signature_b64":"OuHEhfwthmoZ3FWVfZ5zHEU9HDO3441HmnBIRn51/Rawdn0c8LaQ3vNLyc+YudtO0iuxcbEUOsz6JWuBLEYyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0080570d845400cf33c9b1ecedb596839d52666a932bc2cc2cf72c831286447c","last_reissued_at":"2026-05-18T02:31:09.188370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:09.188370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Determining the Solution Space of Vertex-Cover by Interactions and Backbones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Binghui Guo, Renquan Zhang, Wei Wei, Zhiming Zheng","submitted_at":"2011-12-28T08:32:37Z","abstract_excerpt":"To solve the combinatorial optimization problems especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of Vertex-cover, a new structure named interaction between nodes is defined and discovered for random graph, which results in the emergence of the frustration and long-range correlation phenomenon. Based on the backbones and interactions with a node adding process, we propose an Interaction and Backbone Evolution Algorithm to achieve the reduced solution graph, whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6079","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.6079","created_at":"2026-05-18T02:31:09.188476+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.6079v2","created_at":"2026-05-18T02:31:09.188476+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6079","created_at":"2026-05-18T02:31:09.188476+00:00"},{"alias_kind":"pith_short_12","alias_value":"ACAFODMEKQAM","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"ACAFODMEKQAM6M6J","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"ACAFODME","created_at":"2026-05-18T12:26:24.575870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ACAFODMEKQAM6M6JWHWO3NMWQO","json":"https://pith.science/pith/ACAFODMEKQAM6M6JWHWO3NMWQO.json","graph_json":"https://pith.science/api/pith-number/ACAFODMEKQAM6M6JWHWO3NMWQO/graph.json","events_json":"https://pith.science/api/pith-number/ACAFODMEKQAM6M6JWHWO3NMWQO/events.json","paper":"https://pith.science/paper/ACAFODME"},"agent_actions":{"view_html":"https://pith.science/pith/ACAFODMEKQAM6M6JWHWO3NMWQO","download_json":"https://pith.science/pith/ACAFODMEKQAM6M6JWHWO3NMWQO.json","view_paper":"https://pith.science/paper/ACAFODME","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.6079&json=true","fetch_graph":"https://pith.science/api/pith-number/ACAFODMEKQAM6M6JWHWO3NMWQO/graph.json","fetch_events":"https://pith.science/api/pith-number/ACAFODMEKQAM6M6JWHWO3NMWQO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ACAFODMEKQAM6M6JWHWO3NMWQO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ACAFODMEKQAM6M6JWHWO3NMWQO/action/storage_attestation","attest_author":"https://pith.science/pith/ACAFODMEKQAM6M6JWHWO3NMWQO/action/author_attestation","sign_citation":"https://pith.science/pith/ACAFODMEKQAM6M6JWHWO3NMWQO/action/citation_signature","submit_replication":"https://pith.science/pith/ACAFODMEKQAM6M6JWHWO3NMWQO/action/replication_record"}},"created_at":"2026-05-18T02:31:09.188476+00:00","updated_at":"2026-05-18T02:31:09.188476+00:00"}