{"paper":{"title":"Layout of random circulant graphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Israel Rocha, Sebastian Richter","submitted_at":"2017-07-14T12:25:28Z","abstract_excerpt":"A circulant graph H is defined on the set of vertices V=\\left\\{ 1,\\ldots,n\\right\\} and edges E=\\left\\{ \\left(i,j\\right):\\left|i-j\\right|\\equiv s\\left(\\textrm{mod}n\\right),s\\in S\\right\\} , where S\\subseteq\\left\\{ 1,\\ldots,\\lceil\\frac{n-1}{2}\\rceil\\right\\} . A random circulant graph results from deleting edges of H with probability 1-p. We provide a polynomial time algorithm that approximates the solution to the minimum linear arrangement problem for random circulant graphs. We then bound the error of the approximation with high probability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04480","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"}