The model of population protocols provides a universal platform to study distributed processes driven by pairwise interactions of anonymous agents. While population protocols present an elegant and robust model for randomized distributed computation, their efficiency wanes when tackling issues that require more focused communication or the execution of multiple processes. To address this issue, we propose a new, selective variant of population protocols by introducing a partition of the state space and the corresponding conditional selection of responders. We demonstrate on several examples that the new model offers a natural environment, complete with tools and a high-level description, to facilitate more efficient solutions. In particular, we provide fixed-state stable and efficient solutions to two central problems: leader election and majority computation, both with confirmation. This constitutes a separation result, as achieving stable and efficient majority computation requires $\Omega(\log n)$ states in standard population protocols, even when the leader is already determined. Additionally, we explore the computation of the median using the comparison model, where the operational state space of agents is fixed, and the transition function determines the order between (arbitrarily large) hidden keys associated with interacting agents. Our findings reveal that the computation of the median of $n$ numbers requires $\Omega(n)$ time. Moreover, we demonstrate that the problem can be solved in $O(n\log n)$ time, both in expectation and with high probability, in standard population protocols. In contrast, we establish that a feasible solution in selective population protocols can be achieved in $O(\log^4 n)$ time.

翻译：种群协议模型提供了一个通用平台，用于研究由匿名个体间成对交互驱动的分布式过程。尽管种群协议为随机分布式计算提供了优雅且鲁棒的模型，但在处理需要更聚焦通信或多进程执行的问题时，其效率会下降。为解决此问题，我们通过引入状态空间划分及相应的响应者条件选择机制，提出了一种新的选择性种群协议变体。我们通过多个示例表明，该新模型提供了自然的环境，配备工具和高级描述，有助于实现更高效的解决方案。特别地，我们针对两个核心问题——领导者选举和多数计算（均含确认机制）——提供了固定状态、稳定且高效的解决方案。这构成了一个分离性结果，因为在标准种群协议中，即使领导者已确定，实现稳定且高效的多数计算也需要$\Omega(\log n)$个状态。此外，我们利用比较模型探讨了中位数计算问题，其中个体的操作状态空间固定，转移函数决定相关联个体之间的隐藏键（任意大）的顺序。我们的发现表明，计算$n$个数的中位数需要$\Omega(n)$时间。同时，我们证明在标准种群协议中，该问题可以在期望值和高概率下以$O(n\log n)$时间解决。相比之下，我们证实选择性种群协议中可在$O(\log^4 n)$时间内实现可行解。