Consider the scenario where multiple agents have to move in an optimal way through a network, each one towards their ending position while avoiding collisions. By optimal, we mean as fast as possible, which is evaluated by a measure known as the makespan of the proposed solution. This is the setting studied in the Multiagent Path Finding problem. In this work, we additionally provide the agents with a way to communicate with each other. Due to size constraints, it is reasonable to assume that the range of communication of each agent will be limited. What should be the trajectories of the agents to, additionally, maintain a backbone of communication? In this work, we study the Multiagent Path Finding with Communication Constraint problem under the parameterized complexity framework. Our main contribution is three exact algorithms that are efficient when considering particular structures for the input network. We provide such algorithms for the case when the communication range and the number of agents (the makespan resp.) are provided in the input and the network has a tree topology, or bounded maximum degree (has a tree-like topology, i.e., bounded treewidth resp.). We complement these results by showing that it is highly unlikely to construct efficient algorithms when considering the number of agents as part of the input, even if the makespan is $3$ and the communication range is $1$.

翻译：考虑多智能体需要在网络中按最优方式移动的场景，每个智能体需在避免碰撞的前提下到达各自的终点位置。此处"最优"指尽可能快速，其评估标准称为所提方案的完工时间。这正是多智能体路径规划问题所研究的设定。在本工作中，我们额外为智能体提供了相互通信的能力。由于尺寸限制，合理假设每个智能体的通信范围将受到限制。智能体的轨迹应如何规划才能额外维持通信主干网络？本研究在参数化复杂度框架下探讨具有通信约束的多智能体路径规划问题。我们的主要贡献是三种精确算法，这些算法在输入网络具有特定结构时能高效运行。我们针对以下情况提供算法：当通信范围和智能体数量（或完工时间）作为输入参数给出，且网络具有树形拓扑结构，或有界最大度数（即具有树状拓扑结构，即有界树宽）。我们通过证明以下结论来补充这些结果：即使完工时间为$3$且通信范围为$1$，若将智能体数量作为输入参数，则构建高效算法的可能性极低。