{"paper":{"title":"On the homotopy test on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"cs.CG","authors_text":"Francis Lazarus, Julien Rivaud","submitted_at":"2011-10-20T16:30:22Z","abstract_excerpt":"Let G be a graph cellularly embedded in a surface S. Given two closed walks c and d in G, we take advantage of the RAM model to describe linear time algorithms to decide if c and d are homotopic in S, either freely or with fixed basepoint. We restrict S to be orientable for the free homotopy test, but allow non-orientable surfaces when the basepoint is fixed. After O(|G|) time preprocessing independent of c and d, our algorithms answer the homotopy test in O(|c|+|d|) time, where |G|, |c| and |d| are the respective numbers of edges of G, c and d. As a byproduct we obtain linear time algorithms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4573","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"}