We show that there is no subexponential time algorithm for computing the exact solution of the maximum independent set problem in d-regular graphs unless ETH fails. We expand our method to show that it helps to provide lower bounds for other covering problems such as vertex cover and clique. We utilize the construction to show the NP-hardness of MIS on 5-regular planar graphs, closing the exact complexity status of the problem on regular planar graphs.

翻译：我们显示,除非 ETH 失败, 计算 d- regular 图形中最大独立设置问题的确切解决方案没有亚特值时间算法。 我们扩展了方法, 以显示它有助于为顶层覆盖和 clique 等其他覆盖问题提供较低范围。 我们利用构建来显示 MIS 在 5 个常规平面图形上的 NP- 硬度, 从而结束常规平面图形中问题的确切复杂状态 。