{"paper":{"title":"Shortcut sets for the locus of plane Euclidean networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alberto M\\'arquez, Antonio Gonz\\'alez, Delia Garijo, Jos\\'e C\\'aceres, Mar\\'ia Luz Puertas, Paula Ribeiro","submitted_at":"2016-04-13T17:29:09Z","abstract_excerpt":"We study the problem of augmenting the locus $\\mathcal{N}_{\\ell}$ of a plane Euclidean network $\\mathcal{N}$ by inserting iteratively a finite set of segments, called \\emph{shortcut set}, while reducing the diameter of the locus of the resulting network. There are two main differences with the classical augmentation problems: the endpoints of the segments are allowed to be points of $\\mathcal{N}_{\\ell}$ as well as points of the previously inserted segments (instead of only vertices of $\\mathcal{N}$), and the notion of diameter is adapted to the fact that we deal with $\\mathcal{N}_{\\ell}$ inste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03878","kind":"arxiv","version":2},"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"}