{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JA6DRDOKWN4D23VL4ZGU3D6PO2","short_pith_number":"pith:JA6DRDOK","canonical_record":{"source":{"id":"1509.05870","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-19T10:48:31Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"3d5229672e111f4315d94c4d6f044d6be058a26932aac758acd52e990eb53760","abstract_canon_sha256":"d20cc6f914b3a43fb0e1e8f66f995de3ee16e2c267536cd6984197fff55f9807"},"schema_version":"1.0"},"canonical_sha256":"483c388dcab3783d6eabe64d4d8fcf76a045c874efafd4283d1119d67eee2731","source":{"kind":"arxiv","id":"1509.05870","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05870","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05870v1","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05870","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"pith_short_12","alias_value":"JA6DRDOKWN4D","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JA6DRDOKWN4D23VL","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JA6DRDOK","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JA6DRDOKWN4D23VL4ZGU3D6PO2","target":"record","payload":{"canonical_record":{"source":{"id":"1509.05870","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-19T10:48:31Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"3d5229672e111f4315d94c4d6f044d6be058a26932aac758acd52e990eb53760","abstract_canon_sha256":"d20cc6f914b3a43fb0e1e8f66f995de3ee16e2c267536cd6984197fff55f9807"},"schema_version":"1.0"},"canonical_sha256":"483c388dcab3783d6eabe64d4d8fcf76a045c874efafd4283d1119d67eee2731","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:36.479529Z","signature_b64":"pW2QTalaNiH4WzntjpXk+xhkGG+Cx0aUN34SeaW6vlWnOc4qaO3LGau8Cj6WVLTBEfNzdqce9wnsWq2vvoeKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"483c388dcab3783d6eabe64d4d8fcf76a045c874efafd4283d1119d67eee2731","last_reissued_at":"2026-05-18T01:32:36.479099Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:36.479099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.05870","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DjaMOxsG+byGiQMO4VA6Nyt1H9fByuGKxDlXxwOsNTdcFdIHkQU2200GtR/MUZZSGWOHvtrmPUYDnuiwq+tzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:05:04.321020Z"},"content_sha256":"345aa28efe7b913e0aa1b239c9a4e9b1de57f401cda98bc8edcf0b1d12574de9","schema_version":"1.0","event_id":"sha256:345aa28efe7b913e0aa1b239c9a4e9b1de57f401cda98bc8edcf0b1d12574de9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JA6DRDOKWN4D23VL4ZGU3D6PO2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exploiting Reduction Rules and Data Structures: Local Search for Minimum Vertex Cover in Massive Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.DS","authors_text":"Abdul Sattar, Chengqian Li, Ljiljana Brankovic, Vladimir Estivill-Castro, Yi Fan, Zongjie Ma","submitted_at":"2015-09-19T10:48:31Z","abstract_excerpt":"The Minimum Vertex Cover (MinVC) problem is a well-known NP-hard problem. Recently there has been great interest in solving this problem on real-world massive graphs. For such graphs, local search is a promising approach to finding optimal or near-optimal solutions. In this paper we propose a local search algorithm that exploits reduction rules and data structures to solve the MinVC problem in such graphs. Experimental results on a wide range of real-word massive graphs show that our algorithm finds better covers than state-of-the-art local search algorithms for MinVC. Also we present interest"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05870","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y9IKN0kInIygb0s4xBtyyNmjf22iuyEMY3mhXD+vPIzBW4JmJv5mGZkliVB8XQ33aKQ3BOUbo+4abftvAvIwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:05:04.321747Z"},"content_sha256":"e8f7c782b69a164819fbf581b3d3fc8ebad2fcc199f2b2f75e553dfc57430687","schema_version":"1.0","event_id":"sha256:e8f7c782b69a164819fbf581b3d3fc8ebad2fcc199f2b2f75e553dfc57430687"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JA6DRDOKWN4D23VL4ZGU3D6PO2/bundle.json","state_url":"https://pith.science/pith/JA6DRDOKWN4D23VL4ZGU3D6PO2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JA6DRDOKWN4D23VL4ZGU3D6PO2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T12:05:04Z","links":{"resolver":"https://pith.science/pith/JA6DRDOKWN4D23VL4ZGU3D6PO2","bundle":"https://pith.science/pith/JA6DRDOKWN4D23VL4ZGU3D6PO2/bundle.json","state":"https://pith.science/pith/JA6DRDOKWN4D23VL4ZGU3D6PO2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JA6DRDOKWN4D23VL4ZGU3D6PO2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JA6DRDOKWN4D23VL4ZGU3D6PO2","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":"d20cc6f914b3a43fb0e1e8f66f995de3ee16e2c267536cd6984197fff55f9807","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-19T10:48:31Z","title_canon_sha256":"3d5229672e111f4315d94c4d6f044d6be058a26932aac758acd52e990eb53760"},"schema_version":"1.0","source":{"id":"1509.05870","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05870","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05870v1","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05870","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"pith_short_12","alias_value":"JA6DRDOKWN4D","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JA6DRDOKWN4D23VL","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JA6DRDOK","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:e8f7c782b69a164819fbf581b3d3fc8ebad2fcc199f2b2f75e553dfc57430687","target":"graph","created_at":"2026-05-18T01:32:36Z","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":"The Minimum Vertex Cover (MinVC) problem is a well-known NP-hard problem. Recently there has been great interest in solving this problem on real-world massive graphs. For such graphs, local search is a promising approach to finding optimal or near-optimal solutions. In this paper we propose a local search algorithm that exploits reduction rules and data structures to solve the MinVC problem in such graphs. Experimental results on a wide range of real-word massive graphs show that our algorithm finds better covers than state-of-the-art local search algorithms for MinVC. Also we present interest","authors_text":"Abdul Sattar, Chengqian Li, Ljiljana Brankovic, Vladimir Estivill-Castro, Yi Fan, Zongjie Ma","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-19T10:48:31Z","title":"Exploiting Reduction Rules and Data Structures: Local Search for Minimum Vertex Cover in Massive Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05870","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":"sha256:345aa28efe7b913e0aa1b239c9a4e9b1de57f401cda98bc8edcf0b1d12574de9","target":"record","created_at":"2026-05-18T01:32:36Z","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":"d20cc6f914b3a43fb0e1e8f66f995de3ee16e2c267536cd6984197fff55f9807","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-19T10:48:31Z","title_canon_sha256":"3d5229672e111f4315d94c4d6f044d6be058a26932aac758acd52e990eb53760"},"schema_version":"1.0","source":{"id":"1509.05870","kind":"arxiv","version":1}},"canonical_sha256":"483c388dcab3783d6eabe64d4d8fcf76a045c874efafd4283d1119d67eee2731","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"483c388dcab3783d6eabe64d4d8fcf76a045c874efafd4283d1119d67eee2731","first_computed_at":"2026-05-18T01:32:36.479099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:36.479099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pW2QTalaNiH4WzntjpXk+xhkGG+Cx0aUN34SeaW6vlWnOc4qaO3LGau8Cj6WVLTBEfNzdqce9wnsWq2vvoeKBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:36.479529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05870","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:345aa28efe7b913e0aa1b239c9a4e9b1de57f401cda98bc8edcf0b1d12574de9","sha256:e8f7c782b69a164819fbf581b3d3fc8ebad2fcc199f2b2f75e553dfc57430687"],"state_sha256":"01920c1d5f0385b92c894e6820cb2278713930a4266609210cad5e15d49f348d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Pkx48+fDT2EnyWx2UwzgJzSvsGO9w1vzcT6I70ex6dyPGTwJNKu44qiyisqLw84LbrbXZW1y+vY6lp/KyVEAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T12:05:04.325234Z","bundle_sha256":"7f464c029dd8ee3c4fbc4cbde8744812a0b30f4ff40ab23139b583e59ab15229"}}