  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.
