{"paper":{"title":"New Hardness Results for Planar Graph Problems in P and an Algorithm for Sparsest Cut","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Amir Abboud, Philip N. Klein, Vincent Cohen-Addad","submitted_at":"2020-07-05T16:26:27Z","abstract_excerpt":"The Sparsest Cut is a fundamental optimization problem that has been extensively studied. For planar inputs the problem is in $P$ and can be solved in $\\tilde{O}(n^3)$ time if all vertex weights are $1$. Despite a significant amount of effort, the best algorithms date back to the early 90's and can only achieve $O(\\log n)$-approximation in $\\tilde{O}(n)$ time or a constant factor approximation in $\\tilde{O}(n^2)$ time [Rao, STOC92]. Our main result is an $\\Omega(n^{2-\\epsilon})$ lower bound for Sparsest Cut even in planar graphs with unit vertex weights, under the $(min,+)$-Convolution conject"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.02377","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/2007.02377/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"}