We show that certain ways of solving some combinatorial optimization problems can be understood as using query planes to divide the space of problem instances into polyhedra that could fit into those that characterize the problem's various solutions. This viewpoint naturally leads to a splinter-proneness property that is then shown to be responsible for the hardness of the concerned problem. We conjecture that the $NP$-equivalent traveling salesman problem (TSP) has this property and hence is hard to solve to a certain extent.

翻译：我们表明，求解某些组合优化问题的特定方式可被理解为利用查询平面将问题实例空间分割为多面体，这些多面体能够嵌入到刻画问题不同解的特征多面体中。该视角自然地引出一个“易碎性”性质，进而证明该性质是导致所涉问题困难性的根源。我们猜想，与$NP$等价的旅行商问题（TSP）具有此性质，因而在某种程度上难以求解。