{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:G2K46XR57RHWIHGQ2AT6X6V3WC","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":"b95bf7cf0983631ec923759b1f43569008b0e7457715b1def58a8617e37c7646","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-29T05:29:28Z","title_canon_sha256":"e8613ad61a873549af60831ed9c9e16045d08ff3d5fe32d68eb6293a7023ec32"},"schema_version":"1.0","source":{"id":"1111.6698","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6698","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6698v2","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6698","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"pith_short_12","alias_value":"G2K46XR57RHW","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G2K46XR57RHWIHGQ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G2K46XR5","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:0e7002ac649a5a667da4d2332cac980681be9bd02ebcabe8075dd9b1eee26aae","target":"graph","created_at":"2026-05-18T04:07:06Z","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":"In this note, we show that the integrality gap of the $k$-Directed-Component- Relaxation($k$-DCR) LP for the Steiner tree problem, introduced by Byrka, Grandoni, Rothvob and Sanita (STOC 2010), is at most $\\ln(4)<1.39$. The proof is constructive: we can efficiently find a Steiner tree whose cost is at most $\\ln(4)$ times the cost of the optimal fractional $k$-restricted Steiner tree given by the $k$-DCR LP.","authors_text":"Mohammad Taghi Hajiaghayi, Shi Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-29T05:29:28Z","title":"On the Integrality Gap of the Directed-Component Relaxation for Steiner Tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6698","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:eb9a3ad4bed4f3c34caf834feb94d09320271605cee9237a5356cade60d4562f","target":"record","created_at":"2026-05-18T04:07:06Z","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":"b95bf7cf0983631ec923759b1f43569008b0e7457715b1def58a8617e37c7646","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-29T05:29:28Z","title_canon_sha256":"e8613ad61a873549af60831ed9c9e16045d08ff3d5fe32d68eb6293a7023ec32"},"schema_version":"1.0","source":{"id":"1111.6698","kind":"arxiv","version":2}},"canonical_sha256":"3695cf5e3dfc4f641cd0d027ebfabbb08b80455ba8920d0adca6bc9edd416762","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3695cf5e3dfc4f641cd0d027ebfabbb08b80455ba8920d0adca6bc9edd416762","first_computed_at":"2026-05-18T04:07:06.325040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:06.325040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UnvhEs46D+H0xhvCITQ75UMqjE9/NUYJ/QISUDhykE7P69/UIEqaA0UJ9NMNP9TBF+TXpUATlgEmdPKw5JVIDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:06.325510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.6698","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb9a3ad4bed4f3c34caf834feb94d09320271605cee9237a5356cade60d4562f","sha256:0e7002ac649a5a667da4d2332cac980681be9bd02ebcabe8075dd9b1eee26aae"],"state_sha256":"ff5adf7ce8a423f4ffb9329b7ab56e4caf1bcad81dec1e38d3b1cb70538acf9f"}