Multi-agent systems are generally applicable in a wide diversity of domains, such as robot engineering, computer science, the military, and smart cities. In this paper, we introduce a mobile multi-agent sensing problem and present a mathematical formulation. The model can be represented as a submodular maximization problem under a partition matroid constraint, which is NP-hard in general. The optimal solution of the model can be considered computationally intractable. Therefore, we propose two decent algorithms based on the greedy approach, which are global greedy and sequential greedy algorithms, respectively. We show that the sequential greedy algorithm is competitive with the global greedy algorithm and has advantages of computation times. Moreover, we present new approximation ratios of the sequential greedy algorithm and prove tightness of the ratios. Finally, we demonstrate the performances of our results through numerical experiments.

多代理系统通常适用于各种领域，例如机器人工程，计算机科学，军事和智慧城市。在本文中，我们介绍了移动多主体感测问题并提出了数学公式。该模型可以表示为分区拟阵约束下的子模极大化问题，通常为NP-hard。该模型的最佳解决方案可以认为在计算上是难处理的。因此，我们提出了两种基于贪婪方法的体面算法，分别是全局贪婪算法和顺序贪婪算法。我们证明了顺序贪婪算法与全局贪婪算法相比具有竞争优势，并且具有计算时间短的优点。而且，我们提出了顺序贪心算法的新近似比率，并证明了比率的紧密性。最后，我们通过数值实验证明了我们的结果的性能。