{"paper":{"title":"A Sequential Algorithm for Generating Random Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CC","authors_text":"Amin Saberi, Jeong Han Kim, Mohsen Bayati","submitted_at":"2007-02-22T10:00:53Z","abstract_excerpt":"We present a nearly-linear time algorithm for counting and randomly generating simple graphs with a given degree sequence in a certain range. For degree sequence $(d_i)_{i=1}^n$ with maximum degree $d_{\\max}=O(m^{1/4-\\tau})$, our algorithm generates almost uniform random graphs with that degree sequence in time $O(m\\,d_{\\max})$ where $m=\\f{1}{2}\\sum_id_i$ is the number of edges in the graph and $\\tau$ is any positive constant. The fastest known algorithm for uniform generation of these graphs McKay Wormald (1990) has a running time of $O(m^2d_{\\max}^2)$. Our method also gives an independent pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0702124","kind":"arxiv","version":5},"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"}