{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:INYCVT53SPX7HMVOOIRWYDLNX3","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":"df96cfbf4285a1dd078cbc9b722502c5108aea6aa76db0d9a3d01f9c50fdfdce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-01-11T15:39:41Z","title_canon_sha256":"9d4bcc113883ee31283d36b263ec0c2dac219ce2a97c22c4482731d548046010"},"schema_version":"1.0","source":{"id":"1601.02481","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02481","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02481v1","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02481","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"pith_short_12","alias_value":"INYCVT53SPX7","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"INYCVT53SPX7HMVO","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"INYCVT53","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:de3e2be1e9a151cbbd8c81750ae1e2c97049c70301d2735bf960ef64f90643a8","target":"graph","created_at":"2026-05-18T01:23:06Z","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 prize-collecting version of the Node-weighted Steiner Tree problem (NWPCST) restricted to planar graphs. We give a new primal-dual Lagrangian-multiplier-preserving (LMP) 3-approximation algorithm for planar NWPCST. We then show a ($2.88 + \\epsilon$)-approximation which establishes a new best approximation guarantee for planar NWPCST. This is done by combining our LMP algorithm with a threshold rounding technique and utilizing the 2.4-approximation of Berman and Yaroslavtsev for the version without penalties. We also give a primal-dual 4-approximation algorithm for the more general","authors_text":"Carsten Moldenhauer, Jaros{\\l}aw Byrka, Mateusz Lewandowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-01-11T15:39:41Z","title":"Approximation algorithms for node-weighted prize-collecting Steiner tree problems on planar graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02481","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":"sha256:88c8fb4b067d97d466ed79761cc1ebc088dab9f7ede0257ec1d57933600b0900","target":"record","created_at":"2026-05-18T01:23:06Z","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":"df96cfbf4285a1dd078cbc9b722502c5108aea6aa76db0d9a3d01f9c50fdfdce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-01-11T15:39:41Z","title_canon_sha256":"9d4bcc113883ee31283d36b263ec0c2dac219ce2a97c22c4482731d548046010"},"schema_version":"1.0","source":{"id":"1601.02481","kind":"arxiv","version":1}},"canonical_sha256":"43702acfbb93eff3b2ae72236c0d6dbecd877f8681573e483fba30034fcad9cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43702acfbb93eff3b2ae72236c0d6dbecd877f8681573e483fba30034fcad9cc","first_computed_at":"2026-05-18T01:23:06.347582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:06.347582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z5n/1LDabg9Wj/RYpQ3jc8K9Qw4+aK8rA/XA3AyKfkr35TJw9sjQI6zFkIgTOFinJRikPdcu9uumRkePrHwODg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:06.348336Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02481","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88c8fb4b067d97d466ed79761cc1ebc088dab9f7ede0257ec1d57933600b0900","sha256:de3e2be1e9a151cbbd8c81750ae1e2c97049c70301d2735bf960ef64f90643a8"],"state_sha256":"ed8f0e688b784248a6f03accca40315c281a1cd2495cbf8619fc9afafd6a2cef"}