We address the problem of efficient and unobstructed surveillance or communication in complex environments. On one hand, one wishes to use a minimal number of sensors to cover the environment. On the other hand, it is often important to consider solutions that are robust against sensor failure or adversarial attacks. This paper addresses these challenges of designing minimal sensor sets that achieve multi-coverage constraints -- every point in the environment is covered by a prescribed number of sensors. We propose a greedy algorithm to achieve the objective. Further, we explore deep learning techniques to accelerate the evaluation of the objective function formulated in the greedy algorithm. The training of the neural network reveals that the geometric properties of the data significantly impact the network's performance, particularly at the end stage. By taking into account these properties, we discuss the differences in using greedy and $\epsilon$-greedy algorithms to generate data and their impact on the robustness of the network.

翻译：本文针对复杂环境中高效且无遮挡的监控或通信问题展开研究。一方面，我们希望使用最少数量的传感器覆盖整个环境；另一方面，考虑能够抵御传感器故障或恶意攻击的鲁棒方案往往至关重要。本文致力于解决设计满足多重覆盖约束（环境中的每个点均被指定数量的传感器覆盖）的最小传感器集这一挑战。我们提出了一种贪婪算法来实现该目标。此外，我们探索了利用深度学习技术加速贪婪算法中目标函数评估的方法。神经网络训练结果表明，数据几何特性对网络性能具有显著影响，尤其是在训练后期阶段。通过考虑这些特性，我们讨论了使用贪婪算法与ε-贪婪算法生成数据的差异，以及它们对网络鲁棒性的影响。