{"paper":{"title":"Algorithms for low-distortion embeddings into arbitrary 1-dimensional spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Anastasios Sidiropoulos, Daniel Lokshtanov, Fedor V. Fomin, Saket Saurabh, Timothy Carpenter","submitted_at":"2017-12-19T01:52:44Z","abstract_excerpt":"We study the problem of finding a minimum-distortion embedding of the shortest path metric of an unweighted graph into a \"simpler\" metric $X$. Computing such an embedding (exactly or approximately) is a non-trivial task even when $X$ is the metric induced by a path, or, equivalently, into the real line. In this paper we give approximation and fixed-parameter tractable (FPT) algorithms for minimum-distortion embeddings into the metric of a subdivision of some fixed graph $H$, or, equivalently, into any fixed 1-dimensional simplicial complex. More precisely, we study the following problem: For g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06747","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"}