{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IU6LRVV7MQPLYGDROWWLBJZFTT","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":"2274e538bf3e485b3e29849f476224999e2007ff173c993b4bb7986be68746e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-05T11:12:33Z","title_canon_sha256":"8293a81c8d96a03fd635a44bba26bfcdc7d6f39d55c01be8e9a303f1113f5f0b"},"schema_version":"1.0","source":{"id":"1710.01965","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.01965","created_at":"2026-05-17T23:57:50Z"},{"alias_kind":"arxiv_version","alias_value":"1710.01965v4","created_at":"2026-05-17T23:57:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01965","created_at":"2026-05-17T23:57:50Z"},{"alias_kind":"pith_short_12","alias_value":"IU6LRVV7MQPL","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IU6LRVV7MQPLYGDR","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IU6LRVV7","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:fce89da67c6081ec6934fae5ac1ff61371b77f0400cff052ad52a9cfabc1dc79","target":"graph","created_at":"2026-05-17T23:57:50Z","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 \\emph{vitality} of an arc/node of a graph with respect to the maximum flow between two fixed nodes $s$ and $t$ is defined as the reduction of the maximum flow caused by the removal of that arc/node. In this paper we address the issue of determining the vitality of arcs and/or nodes for the maximum flow problem. We show how to compute the vitality of all arcs in a general undirected graph by solving only $2(n-1)$ max flow instances and, In $st$-planar graphs (directed or undirected) we show how to compute the vitality of all arcs and all nodes in $O(n)$ worst-case time. Moreover, after dete","authors_text":"Andrea Ribichini, Giorgio Ausiello, Isabella Lari, Paolo Giulio Franciosa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-05T11:12:33Z","title":"Max flow vitality in general and $st$-planar graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01965","kind":"arxiv","version":4},"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":"sha256:2ffd4ec0c71614a476dd51b6e77a344e5381bc8c18fd41bbe990917fd1b546e9","target":"record","created_at":"2026-05-17T23:57:50Z","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":"2274e538bf3e485b3e29849f476224999e2007ff173c993b4bb7986be68746e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-05T11:12:33Z","title_canon_sha256":"8293a81c8d96a03fd635a44bba26bfcdc7d6f39d55c01be8e9a303f1113f5f0b"},"schema_version":"1.0","source":{"id":"1710.01965","kind":"arxiv","version":4}},"canonical_sha256":"453cb8d6bf641ebc187175acb0a7259cf5875e8dfa28c257bd5f8b35eb5906f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"453cb8d6bf641ebc187175acb0a7259cf5875e8dfa28c257bd5f8b35eb5906f1","first_computed_at":"2026-05-17T23:57:50.912422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:50.912422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FcRpyVZxCfDJgnJf7iV+JxbCh4fcA5qEJwQCXOGOM07RCIUh8cqTTsM0HhlvR5w7t651JnLlZ4VNngDmrtAPDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:50.913045Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.01965","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ffd4ec0c71614a476dd51b6e77a344e5381bc8c18fd41bbe990917fd1b546e9","sha256:fce89da67c6081ec6934fae5ac1ff61371b77f0400cff052ad52a9cfabc1dc79"],"state_sha256":"8b66c1eff207b207314eeec6e0d038119ebad4bdb0386f7006e5912e727fd2c7"}