This is super interesting; how does it compare to other sampling algorithms? While the problem is indeed reducible; it also has a lot more structure than TSP, e

This is super interesting; how does it compare to other sampling algorithms? While the problem is indeed reducible; it also has a lot more structure than TSP, especially if we note that natural images are forced to come from some nice, underlying manifold which is probably very well-behaved. I'd be inclined to believe that with some assumptions on the problem itself (e.g. the images satisfy some smoothness assumptions and of course, assumptions on the objective, itself), we can always come up with a PTAS for this particular instance for any accuracy, ε>0.