{"paper":{"title":"Alternative parameterizations of Metric Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Felix Reidl, Gregory Gutin, Magnus Wahlstr\\\"om, M. S. Ramanujan","submitted_at":"2018-04-27T20:14:11Z","abstract_excerpt":"A set of vertices $W$ in a graph $G$ is called resolving if for any two distinct $x,y\\in V(G)$, there is $v\\in W$ such that ${\\rm dist}_G(v,x)\\neq{\\rm dist}_G(v,y)$, where ${\\rm dist}_G(u,v)$ denotes the length of a shortest path between $u$ and $v$ in the graph $G$. The metric dimension ${\\rm md}(G)$ of $G$ is the minimum cardinality of a resolving set. The Metric Dimension problem, i.e. deciding whether ${\\rm md}(G)\\le k$, is NP-complete even for interval graphs (Foucaud et al., 2017). We study Metric Dimension (for arbitrary graphs) from the lens of parameterized complexity. The problem par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10670","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"}