In this study, a geometric version of an NP-hard problem ("Almost $2-SAT$" problem) is introduced which has potential applications in clustering, separation axis, binary sensor networks, shape separation, image processing, etc. Furthermore, it has been illustrated that the new problem known as "Two Disjoint Convex Hulls" can be solved in polynomial time due to some combinatorial aspects and geometric properties. For this purpose, an $O(n^2)$ algorithm has also been presented which employs the Separating Axis Theorem (SAT) and the duality of points/lines.

翻译：在本研究中,引入了NP-硬性问题的几何版(“近似2美元-SAT$问题”),有可能应用于集群、分离轴、二进制传感器网络、形状分离、图像处理等。此外,还举例说明,由于组合学的某些方面和几几何特性,被称为“两个脱节组合壳”的新问题可以在多元时间内解决。为此,还提出了使用分离轴理论和点/线的双重性(SAT)的$O(n)2)算法。