{"paper":{"title":"Fault Tolerant Approximate BFS Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David Peleg, Merav Parter","submitted_at":"2014-06-24T08:46:12Z","abstract_excerpt":"This paper addresses the problem of designing a {\\em fault-tolerant} $(\\alpha, \\beta)$ approximate BFS structure (or {\\em FT-ABFS structure} for short), namely, a subgraph $H$ of the network $G$ such that subsequent to the failure of some subset $F$ of edges or vertices, the surviving part of $H$ still contains an \\emph{approximate} BFS spanning tree for (the surviving part of) $G$, satisfying $dist(s,v,H\\setminus F) \\leq \\alpha \\cdot dist(s,v,G\\setminus F)+\\beta$ for every $v \\in V$. We first consider {\\em multiplicative} $(\\alpha,0)$ FT-ABFS structures resilient to a failure of a single edge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6169","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"}