An attempt at understanding the difference that makes the sorting problem (the problem solved by sorting algorithms), but not the travelling salesman problem, efficiently solvable, looking at the topologies of their solution spaces.
I think that the best way to think about why some combinatorial problems are hard and others easy isn't to ask what makes a problem hard, but rather what makes a problem easy. Combinatorial problems seem to be hard by default. It takes some special simplifying property to make them easy.