{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FWMLN3RO75PNFC7GRJOQSO7XEG","short_pith_number":"pith:FWMLN3RO","schema_version":"1.0","canonical_sha256":"2d98b6ee2eff5ed28be68a5d093bf721af546f3b345e5af9345db991837bc3b1","source":{"kind":"arxiv","id":"1511.06905","version":1},"attestation_state":"computed","paper":{"title":"A Simple Algorithm For Replacement Paths Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anjeneya Swami Kare","submitted_at":"2015-11-21T17:32:42Z","abstract_excerpt":"Let G=(V,E)(|V|=n and |E|=m) be an undirected graph with positive edge weights. Let P_{G}(s, t) be a shortest s-t path in G. Let l be the number of edges in P_{G}(s, t). The \\emph{Edge Replacement Path} problem is to compute a shortest s-t path in G\\{e}, for every edge e in P_{G}(s, t). The \\emph{Node Replacement Path} problem is to compute a shortest s-t path in G\\{v}, for every vertex v in P_{G}(s, t). In this paper we present an O(T_{SPT}(G)+m+l^2) time and O(m+l^2) space algorithm for both the problems. Where, T_{SPT}(G) is the asymptotic time to compute a single source shortest path tree "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1511.06905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-21T17:32:42Z","cross_cats_sorted":[],"title_canon_sha256":"ecaca420b20e44781543490ac605f3290c8ea47f8c32fb5693745f5cc48c38b5","abstract_canon_sha256":"a8a068b0c43cfe1a9acc18b00ba6ba9416e808c81e68bf5cc7dc193c0d7a9f54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:17.184338Z","signature_b64":"EPQL+5iomXDFWEHVCWVYR+JOqdbXSue+8R7Z4b6UB5OHbCV01N5xahg775IQJ04Twgijzh+ihOcqzcCoYdz8Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d98b6ee2eff5ed28be68a5d093bf721af546f3b345e5af9345db991837bc3b1","last_reissued_at":"2026-05-18T01:26:17.183763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:17.183763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Simple Algorithm For Replacement Paths Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anjeneya Swami Kare","submitted_at":"2015-11-21T17:32:42Z","abstract_excerpt":"Let G=(V,E)(|V|=n and |E|=m) be an undirected graph with positive edge weights. Let P_{G}(s, t) be a shortest s-t path in G. Let l be the number of edges in P_{G}(s, t). The \\emph{Edge Replacement Path} problem is to compute a shortest s-t path in G\\{e}, for every edge e in P_{G}(s, t). The \\emph{Node Replacement Path} problem is to compute a shortest s-t path in G\\{v}, for every vertex v in P_{G}(s, t). In this paper we present an O(T_{SPT}(G)+m+l^2) time and O(m+l^2) space algorithm for both the problems. Where, T_{SPT}(G) is the asymptotic time to compute a single source shortest path tree "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06905","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1511.06905","created_at":"2026-05-18T01:26:17.183842+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.06905v1","created_at":"2026-05-18T01:26:17.183842+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06905","created_at":"2026-05-18T01:26:17.183842+00:00"},{"alias_kind":"pith_short_12","alias_value":"FWMLN3RO75PN","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"FWMLN3RO75PNFC7G","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"FWMLN3RO","created_at":"2026-05-18T12:29:22.688609+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FWMLN3RO75PNFC7GRJOQSO7XEG","json":"https://pith.science/pith/FWMLN3RO75PNFC7GRJOQSO7XEG.json","graph_json":"https://pith.science/api/pith-number/FWMLN3RO75PNFC7GRJOQSO7XEG/graph.json","events_json":"https://pith.science/api/pith-number/FWMLN3RO75PNFC7GRJOQSO7XEG/events.json","paper":"https://pith.science/paper/FWMLN3RO"},"agent_actions":{"view_html":"https://pith.science/pith/FWMLN3RO75PNFC7GRJOQSO7XEG","download_json":"https://pith.science/pith/FWMLN3RO75PNFC7GRJOQSO7XEG.json","view_paper":"https://pith.science/paper/FWMLN3RO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.06905&json=true","fetch_graph":"https://pith.science/api/pith-number/FWMLN3RO75PNFC7GRJOQSO7XEG/graph.json","fetch_events":"https://pith.science/api/pith-number/FWMLN3RO75PNFC7GRJOQSO7XEG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FWMLN3RO75PNFC7GRJOQSO7XEG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FWMLN3RO75PNFC7GRJOQSO7XEG/action/storage_attestation","attest_author":"https://pith.science/pith/FWMLN3RO75PNFC7GRJOQSO7XEG/action/author_attestation","sign_citation":"https://pith.science/pith/FWMLN3RO75PNFC7GRJOQSO7XEG/action/citation_signature","submit_replication":"https://pith.science/pith/FWMLN3RO75PNFC7GRJOQSO7XEG/action/replication_record"}},"created_at":"2026-05-18T01:26:17.183842+00:00","updated_at":"2026-05-18T01:26:17.183842+00:00"}