{"paper":{"title":"Approximate Single Source Dual Fault Tolerant Distance Oracle","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Koustav Das, Manoj Gupta","submitted_at":"2026-07-03T06:33:14Z","abstract_excerpt":"We are given an undirected weighted graph $G$ with $n$ vertices and $m$ edges, edge weights in $[1, W]$, and a designated source vertex $s$. We design a single source dual fault tolerant distance oracle for $G$. Given a destination vertex $t$ and a set $F$ of at most two faulty edges, the oracle returns a $(1 + O(\\epsilon))$-approximation of the weight of the shortest path from the source $s$ to $t$ avoiding $F$. Our oracle uses $\\tilde{O}(n\\sqrt{n})$ space and has $\\tilde{O}(1)$ query time.\n  Prior to our result, single source single fault tolerant oracles were known to return a $(1+\\epsilon)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02999","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.02999/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}