{"paper":{"title":"Polylogarithmic approximation for minimum planarization (almost)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anastasios Sidiropoulos, Ken-ichi Kawarabayashi","submitted_at":"2017-08-15T23:54:36Z","abstract_excerpt":"In the minimum planarization problem, given some $n$-vertex graph, the goal is to find a set of vertices of minimum cardinality whose removal leaves a planar graph. This is a fundamental problem in topological graph theory. We present a $\\log^{O(1)} n$-approximation algorithm for this problem on general graphs with running time $n^{O(\\log n/\\log\\log n)}$. We also obtain a $O(n^\\varepsilon)$-approximation with running time $n^{O(1/\\varepsilon)}$ for any arbitrarily small constant $\\varepsilon > 0$. Prior to our work, no non-trivial algorithm was known for this problem on general graphs, and the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04723","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"}