{"paper":{"title":"Approximating the Integral Fr\\'echet Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Anil Maheshwari, Christian Scheffer, J\\\"org-R\\\"udiger Sack","submitted_at":"2015-12-10T18:31:14Z","abstract_excerpt":"A pseudo-polynomial time $(1 + \\varepsilon)$-approximation algorithm is presented for computing the integral and average Fr\\'{e}chet distance between two given polygonal curves $T_1$ and $T_2$. In particular, the running time is upper-bounded by $\\mathcal{O}( \\zeta^{4}n^4/\\varepsilon^{2})$ where $n$ is the complexity of $T_1$ and $T_2$ and $\\zeta$ is the maximal ratio of the lengths of any pair of segments from $T_1$ and $T_2$. The Fr\\'{e}chet distance captures the minimal cost of a continuous deformation of $T_1$ into $T_2$ and vice versa and defines the cost of a deformation as the maximal d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03359","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"}