{"paper":{"title":"A note on distance labeling in planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Pawe{\\l} Gawrychowski, Przemys{\\l}aw Uzna\\'nski","submitted_at":"2016-11-20T15:32:27Z","abstract_excerpt":"A distance labeling scheme is an assignments of labels, that is binary strings, to all nodes of a graph, so that the distance between any two nodes can be computed from their labels and the labels are as short as possible. A major open problem is to determine the complexity of distance labeling in unweighted and undirected planar graphs. It is known that, in such a graph on $n$ nodes, some labels must consist of $\\Omega(n^{1/3})$ bits, but the best known labeling scheme uses labels of length $O(\\sqrt{n}\\log n)$ [Gavoille, Peleg, P\\'erennes, and Raz, J. Algorithms, 2004]. We show that, in fact,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06529","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"}