Thanks for pointing out there was an attached paper! It seems in section 2.2 the author points out that for a very special case of the snow blower problem, it

Thanks for pointing out there was an attached paper! It seems in section 2.2 the author points out that for a very special case of the snow blower problem, it is np complete ( see section 8 where they show a domain of polygons with holes). This special case might apply to snow blowing narrow paths through a field. Right afterwards, the authors note that > "the hardness of SBP in the fixed-throw model and in simple polygons is open. In fact, we do not even know what the optimal solutions are for simple cases like a square or rectangular domain." which to me says that for the domain similar to an open field, or just a very wide pathway, the problem may be more complicated than NP-complete and they have not yet found an optimal solution for it.