{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6R7QBASWSB2ZIGGRWQNYBO6YF7","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":"b1b6fb5b3e161f1ae47363ae163514352eb1a50d7f78893fade923614fd59e9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-03T16:10:46Z","title_canon_sha256":"9a1c7e83a4660b733d60fdf4e778cdc20885dee9a407b4d991b9def2275922a8"},"schema_version":"1.0","source":{"id":"1807.01260","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01260","created_at":"2026-05-18T00:04:22Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01260v2","created_at":"2026-05-18T00:04:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01260","created_at":"2026-05-18T00:04:22Z"},{"alias_kind":"pith_short_12","alias_value":"6R7QBASWSB2Z","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6R7QBASWSB2ZIGGR","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6R7QBASW","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:96207279520072b343af9d16824a44685383b5d5e78518f5104b6dd32354cfc5","target":"graph","created_at":"2026-05-18T00:04:22Z","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":"Given a 2-edge connected, unweighted, and undirected graph $G$ with $n$ vertices and $m$ edges, a $\\sigma$-tree spanner is a spanning tree $T$ of $G$ in which the ratio between the distance in $T$ of any pair of vertices and the corresponding distance in $G$ is upper bounded by $\\sigma$. The minimum value of $\\sigma$ for which $T$ is a $\\sigma$-tree spanner of $G$ is also called the {\\em stretch factor} of $T$. We address the fault-tolerant scenario in which each edge $e$ of a given tree spanner may temporarily fail and has to be replaced by a {\\em best swap edge}, i.e. an edge that reconnects","authors_text":"Davide Bil\\`o, Kleitos Papadopoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-03T16:10:46Z","title":"A Novel Algorithm for the All-Best-Swap-Edge Problem on Tree Spanners"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01260","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":"sha256:21140e94e7c0b9065357752bdd3f92e72284bd4be27e083c779c4479610cd704","target":"record","created_at":"2026-05-18T00:04:22Z","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":"b1b6fb5b3e161f1ae47363ae163514352eb1a50d7f78893fade923614fd59e9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-03T16:10:46Z","title_canon_sha256":"9a1c7e83a4660b733d60fdf4e778cdc20885dee9a407b4d991b9def2275922a8"},"schema_version":"1.0","source":{"id":"1807.01260","kind":"arxiv","version":2}},"canonical_sha256":"f47f00825690759418d1b41b80bbd82fdb153fe7a355ef661080b28adcaf80d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f47f00825690759418d1b41b80bbd82fdb153fe7a355ef661080b28adcaf80d9","first_computed_at":"2026-05-18T00:04:22.631248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:22.631248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZDDk0sfYDO5HAIdr0LbT/MwQDFRslFp8qY3IrNVUpUISjHCMs5f/8AhSw3NXbccW82+UG2XUjibfqmJ9ZUnMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:22.631813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.01260","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21140e94e7c0b9065357752bdd3f92e72284bd4be27e083c779c4479610cd704","sha256:96207279520072b343af9d16824a44685383b5d5e78518f5104b6dd32354cfc5"],"state_sha256":"6f9cd4d5db17b86dec857786a9654decec61bb6852a699d11bd77f3482d4819b"}