{"paper":{"title":"Quasi-polynomial time approximation schemes for packing and covering problems in planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andreas Wiese, Erik Jan van Leeuwen, Micha{\\l} Pilipczuk","submitted_at":"2018-07-19T20:00:44Z","abstract_excerpt":"We consider two optimization problems in planar graphs. In Maximum Weight Independent Set of Objects we are given a graph $G$ and a family $\\mathcal{D}$ of objects, each being a connected subgraph of $G$ with a prescribed weight, and the task is to find a maximum-weight subfamily of $\\mathcal{D}$ consisting of pairwise disjoint objects. In Minimum Weight Distance Set Cover we are given an edge-weighted graph $G$, two sets $\\mathcal{D},\\mathcal{C}$ of vertices of $G$, where vertices of $\\mathcal{D}$ have prescribed weights, and a nonnegative radius $r$. The task is to find a minimum-weight subs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07626","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"}