{"paper":{"title":"Inserting Multiple Edges into a Planar Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Markus Chimani, Petr Hlin\\v{e}n\\'y","submitted_at":"2015-09-26T09:02:35Z","abstract_excerpt":"Let $G$ be a connected planar (but not yet embedded) graph and $F$ a set of additional edges not yet in $G$. The {multiple edge insertion} problem (MEI) asks for a drawing of $G+F$ with the minimum number of pairwise edge crossings, such that the subdrawing of $G$ is plane. An optimal solution to this problem approximates the crossing number of the graph $G+F$.\n  Finding an exact solution to MEI is NP-hard for general $F$, but linear time solvable for the special case of $|F|=1$ (SODA01, Algorithmica) or when all of $F$ are incident to a new vertex (SODA09).\n  The complexity for general $F$ bu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07952","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"}