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The fault tolerant subgraph for any graph problem maintains a sparse subgraph $H$ of $G$, such that for any set $F$ of $k$ failures, the solution for the graph problem on $G\\setminus F$ is maintained in $H\\setminus F$. We address the problem of maintaining a fault tolerant subgraph for Breath First Search tree (BFS) of the graph from a single source $s\\in V$ (referred as $k$ FT-BFS) or multiple sources $S\\subseteq V$ (referred as $k$ FT-MBFS).\n  The problem of $k$ FT-BFS was firs"},"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":"1704.06907","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-23T10:40:00Z","cross_cats_sorted":[],"title_canon_sha256":"c783b53a76a4719a5da20e0002c4d2698e0bc942c40afd1e319ee16aefd3d468","abstract_canon_sha256":"aeb6e96038d8f04bbe3ad45ed1b2944670bbff4778237f705e01116b996fb52c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:55.417276Z","signature_b64":"CCEUZAMVCriW34t8SmxGv4uxmbBRqwkFlnvrZ0rrSv5HdCRL1byZSW/osanx9DC50kOqRJ5nAGR6kHlW+8o0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"351491c58827e52c775546f937c8f24380b7e6c07115dadbdf33032c9a7991b8","last_reissued_at":"2026-05-18T00:45:55.416571Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:55.416571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiple Source Dual Fault Tolerant BFS Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Manoj Gupta, Shahbaz Khan","submitted_at":"2017-04-23T10:40:00Z","abstract_excerpt":"Let $G=(V,E)$ be a graph with $n$ vertices and $m$ edges, with a designated set of $\\sigma$ sources $S\\subseteq V$. The fault tolerant subgraph for any graph problem maintains a sparse subgraph $H$ of $G$, such that for any set $F$ of $k$ failures, the solution for the graph problem on $G\\setminus F$ is maintained in $H\\setminus F$. We address the problem of maintaining a fault tolerant subgraph for Breath First Search tree (BFS) of the graph from a single source $s\\in V$ (referred as $k$ FT-BFS) or multiple sources $S\\subseteq V$ (referred as $k$ FT-MBFS).\n  The problem of $k$ FT-BFS was firs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06907","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":"1704.06907","created_at":"2026-05-18T00:45:55.416687+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.06907v1","created_at":"2026-05-18T00:45:55.416687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06907","created_at":"2026-05-18T00:45:55.416687+00:00"},{"alias_kind":"pith_short_12","alias_value":"GUKJDRMIE7SS","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GUKJDRMIE7SSY52V","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GUKJDRMI","created_at":"2026-05-18T12:31:18.294218+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/GUKJDRMIE7SSY52VI34TPSHSIO","json":"https://pith.science/pith/GUKJDRMIE7SSY52VI34TPSHSIO.json","graph_json":"https://pith.science/api/pith-number/GUKJDRMIE7SSY52VI34TPSHSIO/graph.json","events_json":"https://pith.science/api/pith-number/GUKJDRMIE7SSY52VI34TPSHSIO/events.json","paper":"https://pith.science/paper/GUKJDRMI"},"agent_actions":{"view_html":"https://pith.science/pith/GUKJDRMIE7SSY52VI34TPSHSIO","download_json":"https://pith.science/pith/GUKJDRMIE7SSY52VI34TPSHSIO.json","view_paper":"https://pith.science/paper/GUKJDRMI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.06907&json=true","fetch_graph":"https://pith.science/api/pith-number/GUKJDRMIE7SSY52VI34TPSHSIO/graph.json","fetch_events":"https://pith.science/api/pith-number/GUKJDRMIE7SSY52VI34TPSHSIO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GUKJDRMIE7SSY52VI34TPSHSIO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GUKJDRMIE7SSY52VI34TPSHSIO/action/storage_attestation","attest_author":"https://pith.science/pith/GUKJDRMIE7SSY52VI34TPSHSIO/action/author_attestation","sign_citation":"https://pith.science/pith/GUKJDRMIE7SSY52VI34TPSHSIO/action/citation_signature","submit_replication":"https://pith.science/pith/GUKJDRMIE7SSY52VI34TPSHSIO/action/replication_record"}},"created_at":"2026-05-18T00:45:55.416687+00:00","updated_at":"2026-05-18T00:45:55.416687+00:00"}