{"paper":{"title":"On constant multi-commodity flow-cut gaps for directed minor-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anastasios Sidiropoulos, Ario Salmasi, Vijay Sridhar","submitted_at":"2017-11-04T00:38:57Z","abstract_excerpt":"The multi-commodity flow-cut gap is a fundamental parameter that affects the performance of several divide \\& conquer algorithms, and has been extensively studied for various classes of undirected graphs. It has been shown by Linial, London and Rabinovich \\cite{linial1994geometry} and by Aumann and Rabani \\cite{aumann1998log} that for general $n$-vertex graphs it is bounded by $O(\\log n)$ and the Gupta-Newman-Rabinovich-Sinclair conjecture \\cite{gupta2004cuts} asserts that it is $O(1)$ for any family of graphs that excludes some fixed minor.\n  The flow-cut gap is poorly understood for the case"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01370","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"}