
Snowblowing is NP-complete - johndcook
https://punkrockor.wordpress.com/2015/02/09/snowblowing-is-np-complete/
======
douche
I don't understand the reference to lawn-mowing being NP-complete - I thought
I had a good algorithm: mow once around the outside, blowing grass inward, to
get the edges without hitting things with the exhaust chute, then afterwards
mow concentrically, blowing grass outward. Once the width is less than the
turning radius of the mower, switch to only mowing along the long axis of the
area.

Now, when there are rocks, stumps or trees within the area things get more
interesting, depending on your tolerance for having to sharpen the blades...

~~~
gchpaco
Yards are generally not in shapes that look like mazes crossed with Hilbert
space filling curves, which the problem statement permits.

------
rcthompson
Now I feel less bad about the vague suspicion that I was mowing my dad's lawn
suboptimally for all those years.

------
amelius
Reminds me of Sokoban, which is NP-hard [1]

[1]
[http://en.wikipedia.org/wiki/Sokoban](http://en.wikipedia.org/wiki/Sokoban)

------
snissn
I don't think the author understands what np complete actually means. I don't
think that it is easy to verify that a snow Blown path is optimally efficient.
It's interesting to discuss the complexity of day to day tasks, but optimal
cleaning seems to be np hard, not np complete. You may think that you have the
optimal solution until a friend of yours shows you his solution.

~~~
kcl
The author uses NP-complete correctly. Section 2.2 of the paper establishes
the problem is in NP and not merely NP-hard.

Your intuition about verifying optimal solutions has misled you here.
Interesting optimization questions such as "shortest" or "best" are
conventionally reformulated as decision questions about a particular bound.
The verification then becomes easy: check to see, for instance, that the
certificate path works and is shorter than the specified bound. A log-time
search with such a verifier as a subroutine produces a polynomial verifier for
the original optimality question.

~~~
snissn
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.

------
exabrial
What if you're raking wind rows... how does that affect the mowing problem? :)

