{"paper":{"title":"Low-Cost Arborescence Under Edge Faults","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A subgraph of size O(n^{3/2}) lets you recover a 2-approximate min-cost arborescence after any single edge fault.","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Dipan Dey, Telikepalli Kavitha","submitted_at":"2026-05-13T17:21:08Z","abstract_excerpt":"Our input is a directed graph $G = (V,E)$ on $n$ vertices and $m$ edges with a designated root vertex $r$ and a function $cost: E \\rightarrow \\mathbb{R}_{\\geq 0}$. The problem is to maintain a min-cost arborescence in $G$ in the presence of edge faults (a single fault at a time). Edge faults are transient and once the faulty edge is repaired, the original min-cost arborescence $\\mathcal{T}$ is restored. Whenever an edge fault happens, we need to update $\\mathcal{T}$ to a min-cost arborescence in $G-f$, where $f$ is the faulty edge. Since computing a min-cost arborescence in $G - f$ takes $O(m "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show a simple polynomial-time algorithm to construct a subgraph H of size O(n^{3/2}) such that, for any f in E, a min-cost arborescence in H-f is a 2-approximation of a min-cost arborescence in G-f.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That a min-cost arborescence can be computed efficiently inside the constructed subgraph H-f and that the 2-approximation guarantee holds for the specific construction given in the full paper.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"An O(n^{3/2})-size subgraph preserves 2-approximate min-cost arborescences under single edge faults with fast updates, plus a tight k times rank bound for k-fault-tolerant matroid preservers.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A subgraph of size O(n^{3/2}) lets you recover a 2-approximate min-cost arborescence after any single edge fault.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ecfcd56a319dd5a59dac7b199a7bee27d28a5fdc3d9a4646b7f57dc750ba8bb5"},"source":{"id":"2605.13800","kind":"arxiv","version":1},"verdict":{"id":"c855fa24-c0bc-43a2-b19a-383a5c7a3f0a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:31:49.790446Z","strongest_claim":"We show a simple polynomial-time algorithm to construct a subgraph H of size O(n^{3/2}) such that, for any f in E, a min-cost arborescence in H-f is a 2-approximation of a min-cost arborescence in G-f.","one_line_summary":"An O(n^{3/2})-size subgraph preserves 2-approximate min-cost arborescences under single edge faults with fast updates, plus a tight k times rank bound for k-fault-tolerant matroid preservers.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That a min-cost arborescence can be computed efficiently inside the constructed subgraph H-f and that the 2-approximation guarantee holds for the specific construction given in the full paper.","pith_extraction_headline":"A subgraph of size O(n^{3/2}) lets you recover a 2-approximate min-cost arborescence after any single edge fault."},"references":{"count":25,"sample":[{"doi":"10.1007/978-3-662-48653-5_35","year":2015,"title":"Fault tolerant reachability for directed graphs","work_id":"75868f8a-1b4f-44eb-a6f4-04a5f24396c9","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"Fault-tolerant subgraph for single-source reachability: General and optimal.SIAM Journal on Computing, 47(1):80–95, 2018","work_id":"8117ad94-0743-47f1-87fc-ff7d4e7c5d90","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/s00453-012-9621-y","year":2013,"title":"2 BLM12 Surender Baswana, Utkarsh Lath, and Anuradha S","work_id":"f39237b1-bf57-4d15-9cd1-f73bf0a99787","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Matthias Bentert, Fedor V . Fomin, Petr A. Golovach, and Laure Morelle. Fault-tolerant matroid bases. InProceedings of the 33rd Annual European Symposium on Algorithms, (ESA 2025), pages 83:1–83:14,","work_id":"22b00ba5-a162-449f-98af-4259ab32a73c","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.4230/lipics.esa.2025.83","year":2025,"title":"URL: https://doi.org/10.4230/LIPIcs.ESA.2025.83, doi:10.4230/LIPICS. ESA.2025.83","work_id":"fcbb6e3c-bc47-4e86-955c-2179f0dbc1c9","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":25,"snapshot_sha256":"04ff9ce52820990adb13723a00bea9e6ea79c4c156498dba588b79415f27a099","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"c16b9043e654a6dd8b49b3c98970f36ea03394b081703eca699be4b7052c8501"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}