{"paper":{"title":"The Information Flow Problem on Clock Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ross Atkins","submitted_at":"2016-05-17T22:44:20Z","abstract_excerpt":"The information flow problem on a network asks whether $r$ senders, $v_1,v_2, \\ldots ,v_r$ can each send messages to $r$ corresponding receivers $v_{n+1}, \\ldots ,v_{n+r}$ via intermediate nodes $v_{r+1}, \\ldots ,v_n$. For a given finite $R \\subset \\mathbb{Z}^+$, the clock network $N_n(R)$ has edge $v_iv_k$ if and only if $k>r$ and $k-i \\in R$. We show that the information flow problem on $N_n(\\{1,2, \\ldots ,r\\})$ can be solved for all $n \\geq r$. We also show that for any finite $R$ such that $\\gcd(R)=1$ and $r = \\max(R)$, we show that the information flow problem can be solved on $N_n(R)$ fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05391","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"}