{"paper":{"title":"Embedding multidimensional grids into optimal hypercubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Pritikin, I.H. Sudborough, Zevi Miller","submitted_at":"2014-03-11T20:45:51Z","abstract_excerpt":"Let $G$ and $H$ be graphs, with $|V(H)|\\geq |V(G)| $, and $f:V(G)\\rightarrow V(H)$ a one to one map of their vertices. Let $dilation(f) = max\\{ dist_{H}(f(x),f(y)): xy\\in E(G) \\}$, where $dist_{H}(v,w)$ is the distance between vertices $v$ and $w$ of $H$. Now let $B(G,H)$ = $min_{f}\\{ dilation(f) \\}$, over all such maps $f$.\n  The parameter $B(G,H)$ is a generalization of the classic and well studied \"bandwidth\" of $G$, defined as $B(G,P(n))$, where $P(n)$ is the path on $n$ points and $n = |V(G)|$. Let $[a_{1}\\times a_{2}\\times \\cdots \\times a_{k} ]$ be the $k$-dimensional grid graph with int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2749","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"}