{"paper":{"title":"Efficient construction of broadcast graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"A. Averbuch, R. Hollander Shabtai, Y. Roditty","submitted_at":"2013-12-05T12:41:45Z","abstract_excerpt":"A broadcast graph is a connected graph, $G=(V,E)$, $ |V |=n$, in which each vertex can complete broadcasting of one message within at most $t=\\lceil \\log n\\rceil$ time units. A minimum broadcast graph on $n$ vertices is a broadcast graph with the minimum number of edges over all broadcast graphs on $n$ vertices. The cardinality of the edge set of such a graph is denoted by $B(n)$. In this paper we construct a new broadcast graph with\n  $B(n) \\le (k+1)N -(t-\\frac{k}{2}+2)2^{k}+t-k+2$, for $n=N=(2^{k}-1)2^{t+1-k}$ and\n  $B(n) \\le (k+1-p)n -(t-\\frac{k}{2}+p+2)2^{k}+t-k -(p-2)2^{p}$, for $2^{t} < "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1523","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"}