Broadcasting is an information dissemination primitive where a message originates at a node (called the originator) and is passed to all other nodes in the network. Broadcasting research is motivated by efficient network design and determining the broadcast times of standard network topologies. Verifying the broadcast time of a node $v$ in an arbitrary network $G$ is known to be NP-hard. Additionally, recent findings show that the broadcast time problem is NP-hard in several highly restricted subfamilies of cactus graphs. The most restrictive of these families is known as \emph{$k$-cycle graphs} or \emph{flower graphs} and is the focus of this paper. We present a simple $(1.5-ε)$-approximation algorithm for determining the broadcast time of networks modeled using $k$-cycle graphs, where $ε> 0$ depends on the structure of the graph.

翻译：广播是一种信息传播原语：信息从一个节点（称为源节点）产生，并传递给网络中所有其他节点。广播研究源于高效网络设计以及确定标准网络拓扑中广播时间的需求。验证任意网络$G$中节点$v$的广播时间已被证明是NP困难问题。此外，最新研究表明，在几个高度受限的仙人掌图子族中，广播时间问题也是NP困难的。这些子族中限制最严格的一类被称为\emph{k-路图}或\emph{花卉图}，这也是本文的研究重点。我们提出了一种简单的$(1.5-ε)$-近似算法，用于确定基于$k$-路图建模的网络的广播时间，其中$ε> 0$取决于图的结构。