{"paper":{"title":"Planar Steiner Orientation is NP-complete","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"cs.DM","authors_text":"Andre L\\\"offler, Johannes Blum, Johannes Zink, Moritz Beck, Myroslav Kryven","submitted_at":"2018-04-20T08:57:39Z","abstract_excerpt":"Many applications in graph theory are motivated by routing or flow problems. Among these problems is Steiner Orientation: given a mixed graph G (having directed and undirected edges) and a set T of k terminal pairs in G, is there an orientation of the undirected edges in G such that there is a directed path for every terminal pair in T ? This problem was shown to be NP -complete by Arkin and Hassin [1] and later W [1]-hard by Pilipczuk and Wahlstr\\\"om [7], parametrized by k. On the other hand, there is an XP algorithm by Cygan et al. [3] and a polynomial time algorithm for graphs without direc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07496","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"}