{"paper":{"title":"Computing upper bounds for optimal density of $(t,r)$ broadcasts on the infinite grid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjamin F. Drews, Pamela E. Harris, Timothy W. Randolph","submitted_at":"2017-12-01T01:54:01Z","abstract_excerpt":"The domination number of a finite graph $G$ with vertex set $V$ is the cardinality of the smallest set $S\\subseteq V$ such that for every vertex $v\\in V$ either $v\\in S$ or $v$ is adjacent to a vertex in $S$. A set $S$ satisfying these conditions is called a dominating set. In 2015 Blessing, Insko, Johnson, and Mauretour introduced $(t,r)$ broadcast domination, a generalization of graph domination parameterized by the nonnegative integers $t$ and $r$. In this setting, we say that the signal a vertex $v\\in V$ receives from a tower of strength $t$ located at vertex $T$ is defined by $sig(v,T)=ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00150","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"}