The task of the broadcast problem is, given a graph G and a source vertex s, to compute the minimum number of rounds required to disseminate a piece of information from s to all vertices in the graph. It is assumed that, at each round, an informed vertex can transmit the information to at most one of its neighbors. The broadcast problem is known to NP-hard. We show that the problem is FPT when parametrized by the size k of a feedback edge-set, or by the size k of a vertex-cover, or by k=n-t where t is the input deadline for the broadcast protocol to complete.

翻译：广播问题的任务是：给定一个图G和一个源顶点s，计算将一条信息从s传播到图中所有顶点所需的最少轮数。假设在每一轮中，一个已知信息的顶点最多可以向其一个邻居传输该信息。广播问题已知是NP难的。我们证明，当问题参数化为反馈边集的大小k、顶点覆盖的大小k或k=n-t（其中t是广播协议完成的输入截止时间）时，该问题是固定参数可解的（FPT）。