{"paper":{"title":"FPT algorithms for embedding into low complexity graphic metrics","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Arijit Ghosh, Gopinath Mishra, Sudeshna Kolay","submitted_at":"2018-01-10T07:19:58Z","abstract_excerpt":"The Metric Embedding problem takes as input two metric spaces $(X,D_X)$ and $(Y,D_Y)$, and a positive integer $d$. The objective is to determine whether there is an embedding $F:X \\rightarrow Y$ such that $d_{F} \\leq d$, where $d_{F}$ denotes the distortion of the map $F$. Such an embedding is called a distortion $d$ embedding. The bijective Metric Embedding problem is a special case of the Metric Embedding problem where $|X| = |Y|$. In parameterized complexity, the Metric Embedding problem, in full generality, is known to be W-hard and therefore, not expected to have an FPT algorithm. In this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03253","kind":"arxiv","version":3},"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"}