{"paper":{"title":"The $k$-Fr\\'echet distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Hugo A Akitaya, J\\'er\\^ome Urhausen, Leonie Ryvkin, Maike Buchin","submitted_at":"2019-03-06T13:14:02Z","abstract_excerpt":"We introduce a new distance measure for comparing polygonal chains: the $k$-Fr\\'echet distance. As the name implies, it is closely related to the well-studied Fr\\'echet distance but detects similarities between curves that resemble each other only piecewise. The parameter $k$ denotes the number of subcurves into which we divide the input curves. The $k$-Fr\\'echet distance provides a nice transition between (weak) Fr\\'echet distance and Hausdorff distance. However, we show that deciding this distance measure turns out to be NP-complete, which is interesting since both (weak) Fr\\'echet and Hausd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02353","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"}