{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EA23EUUWOXLK7SF2S2YU7E7G6Q","short_pith_number":"pith:EA23EUUW","canonical_record":{"source":{"id":"1801.00313","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-12-31T16:48:56Z","cross_cats_sorted":[],"title_canon_sha256":"1233be03cc47f08953122fedb58957d75620fca40c614eb16f2e7cfd90b7fefa","abstract_canon_sha256":"d52caceaf5f36845a82be9c70493a8288011f1c3eca29631a23de6f5871ff08c"},"schema_version":"1.0"},"canonical_sha256":"2035b2529675d6afc8ba96b14f93e6f42e047235b59f824b8aacdf27b1e2ab20","source":{"kind":"arxiv","id":"1801.00313","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00313","created_at":"2026-05-18T00:16:36Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00313v2","created_at":"2026-05-18T00:16:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00313","created_at":"2026-05-18T00:16:36Z"},{"alias_kind":"pith_short_12","alias_value":"EA23EUUWOXLK","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EA23EUUWOXLK7SF2","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EA23EUUW","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EA23EUUWOXLK7SF2S2YU7E7G6Q","target":"record","payload":{"canonical_record":{"source":{"id":"1801.00313","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-12-31T16:48:56Z","cross_cats_sorted":[],"title_canon_sha256":"1233be03cc47f08953122fedb58957d75620fca40c614eb16f2e7cfd90b7fefa","abstract_canon_sha256":"d52caceaf5f36845a82be9c70493a8288011f1c3eca29631a23de6f5871ff08c"},"schema_version":"1.0"},"canonical_sha256":"2035b2529675d6afc8ba96b14f93e6f42e047235b59f824b8aacdf27b1e2ab20","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:36.532582Z","signature_b64":"IGg9kKuI1UsHC6Hjrz8sllhBNno1epPw2kQ4s01Wqq1B/0FBn4Zi4YIBF0u+716+kRqrp7reKzjQbI2I6rCSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2035b2529675d6afc8ba96b14f93e6f42e047235b59f824b8aacdf27b1e2ab20","last_reissued_at":"2026-05-18T00:16:36.531992Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:36.531992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.00313","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:16:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kYRDEz61ANOQz3b0zohX0I1uu4RqcggrHrUpNDggsQJ2faTJ2qelxvWGwrVqTkpJzs8lCBy2n0IzQsEfFobhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T03:47:10.233541Z"},"content_sha256":"a4283cef8ee34127f4f6ed63db0ea6a491bc95c338cd883a3dd22a60508dfe4a","schema_version":"1.0","event_id":"sha256:a4283cef8ee34127f4f6ed63db0ea6a491bc95c338cd883a3dd22a60508dfe4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EA23EUUWOXLK7SF2S2YU7E7G6Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximating Node-Weighted k-MST on Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jaros{\\l}aw Byrka, Joachim Spoerhase, Mateusz Lewandowski","submitted_at":"2017-12-31T16:48:56Z","abstract_excerpt":"We study the problem of finding a minimum weight connected subgraph spanning at least $k$ vertices on planar, node-weighted graphs. We give a $(4+\\eps)$-approximation algorithm for this problem. We achieve this by utilizing the recent LMP primal-dual $3$-approximation for the node-weighted prize-collecting Steiner tree problem by Byrka et al (SWAT'16) and adopting an approach by Chudak et al. (Math.\\ Prog.\\ '04) regarding Lagrangian relaxation for the edge-weighted variant. In particular, we improve the procedure of picking additional vertices (tree merging procedure) given by Sadeghian (2013)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00313","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:16:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SXCAYgBR1LaoXC9bb4HlIhivCu54zcz4vEdtZRtOXFiC5m0mlZNdG7DaXs4F8n7j0DLgiaAPRkyUFFXkrVDqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T03:47:10.233916Z"},"content_sha256":"82d3730a4969c014312043bd5dd06c7db5544c342db9b67c806e5b25b835ae5c","schema_version":"1.0","event_id":"sha256:82d3730a4969c014312043bd5dd06c7db5544c342db9b67c806e5b25b835ae5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EA23EUUWOXLK7SF2S2YU7E7G6Q/bundle.json","state_url":"https://pith.science/pith/EA23EUUWOXLK7SF2S2YU7E7G6Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EA23EUUWOXLK7SF2S2YU7E7G6Q/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":"2026-06-25T03:47:10Z","links":{"resolver":"https://pith.science/pith/EA23EUUWOXLK7SF2S2YU7E7G6Q","bundle":"https://pith.science/pith/EA23EUUWOXLK7SF2S2YU7E7G6Q/bundle.json","state":"https://pith.science/pith/EA23EUUWOXLK7SF2S2YU7E7G6Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EA23EUUWOXLK7SF2S2YU7E7G6Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EA23EUUWOXLK7SF2S2YU7E7G6Q","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":"d52caceaf5f36845a82be9c70493a8288011f1c3eca29631a23de6f5871ff08c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-12-31T16:48:56Z","title_canon_sha256":"1233be03cc47f08953122fedb58957d75620fca40c614eb16f2e7cfd90b7fefa"},"schema_version":"1.0","source":{"id":"1801.00313","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00313","created_at":"2026-05-18T00:16:36Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00313v2","created_at":"2026-05-18T00:16:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00313","created_at":"2026-05-18T00:16:36Z"},{"alias_kind":"pith_short_12","alias_value":"EA23EUUWOXLK","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EA23EUUWOXLK7SF2","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EA23EUUW","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:82d3730a4969c014312043bd5dd06c7db5544c342db9b67c806e5b25b835ae5c","target":"graph","created_at":"2026-05-18T00:16:36Z","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":"We study the problem of finding a minimum weight connected subgraph spanning at least $k$ vertices on planar, node-weighted graphs. We give a $(4+\\eps)$-approximation algorithm for this problem. We achieve this by utilizing the recent LMP primal-dual $3$-approximation for the node-weighted prize-collecting Steiner tree problem by Byrka et al (SWAT'16) and adopting an approach by Chudak et al. (Math.\\ Prog.\\ '04) regarding Lagrangian relaxation for the edge-weighted variant. In particular, we improve the procedure of picking additional vertices (tree merging procedure) given by Sadeghian (2013)","authors_text":"Jaros{\\l}aw Byrka, Joachim Spoerhase, Mateusz Lewandowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-12-31T16:48:56Z","title":"Approximating Node-Weighted k-MST on Planar Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00313","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:a4283cef8ee34127f4f6ed63db0ea6a491bc95c338cd883a3dd22a60508dfe4a","target":"record","created_at":"2026-05-18T00:16:36Z","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":"d52caceaf5f36845a82be9c70493a8288011f1c3eca29631a23de6f5871ff08c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-12-31T16:48:56Z","title_canon_sha256":"1233be03cc47f08953122fedb58957d75620fca40c614eb16f2e7cfd90b7fefa"},"schema_version":"1.0","source":{"id":"1801.00313","kind":"arxiv","version":2}},"canonical_sha256":"2035b2529675d6afc8ba96b14f93e6f42e047235b59f824b8aacdf27b1e2ab20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2035b2529675d6afc8ba96b14f93e6f42e047235b59f824b8aacdf27b1e2ab20","first_computed_at":"2026-05-18T00:16:36.531992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:36.531992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IGg9kKuI1UsHC6Hjrz8sllhBNno1epPw2kQ4s01Wqq1B/0FBn4Zi4YIBF0u+716+kRqrp7reKzjQbI2I6rCSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:36.532582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00313","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4283cef8ee34127f4f6ed63db0ea6a491bc95c338cd883a3dd22a60508dfe4a","sha256:82d3730a4969c014312043bd5dd06c7db5544c342db9b67c806e5b25b835ae5c"],"state_sha256":"bf3cf22eeef387633f7ddc8d11c9b92d67d7c310997b504a9056d61e14d2bc7f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V3MNBfr9LVD1WW3dooJxZuA6fZTREzDfxo4o4PXdMi6+/bB7iCfsyclhLyvUU5sEtRZUhrDjAGGpqDpCG2nEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T03:47:10.235851Z","bundle_sha256":"1f3d0f9fc3a8ad7f3b0741bf5b867d518dc77f7889d7913635dfbe8a4ce16747"}}