{"paper":{"title":"Towards single face shortest vertex-disjoint paths in undirected planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Amir Nayyeri, Farzad Zafarani, Glencora Borradaile","submitted_at":"2015-07-21T20:20:10Z","abstract_excerpt":"Given $k$ pairs of terminals $\\{(s_{1}, t_{1}), \\ldots, (s_{k}, t_{k})\\}$ in a graph $G$, the min-sum $k$ vertex-disjoint paths problem is to find a collection $\\{Q_{1}, Q_{2}, \\ldots, Q_{k}\\}$ of vertex-disjoint paths with minimum total length, where $Q_{i}$ is an $s_i$-to-$t_i$ path between $s_i$ and $t_i$. We consider the problem in planar graphs, where little is known about computational tractability, even in restricted cases. Kobayashi and Sommer propose a polynomial-time algorithm for $k \\le 3$ in undirected planar graphs assuming all terminals are adjacent to at most two faces. Colin de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05980","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"}