Algorithm for cleaning some spots on a floor using automatic vacuum cleaners?

This looks like the travelling salesman problem to me. But I'm sure there are faster ways to get a result close to the optimal solution Hopefully this gives you something to start searching with.

This looks like the travelling salesman problem to me. But I'm sure there are faster ways to get a result close to the optimal solution. Hopefully this gives you something to start searching with.

I hope it doesn't look like that, that problem is hard! ;) If we consider 'n'=1 cleaner and 'k' spots to clean you might be right but since I could also have 'n' > 'k' here things seem pretty different. I'm still trying to understand if having 'multiple salesman' makes the problem harder or easier... thanks!

– Gevorg Oct 28 at 2:46 I think it's not quite TSP, but possibly related, since you have k 'towns' to be visited by n 'salesmen'. So we can think of it as n TSPs (possibly conducted in parallel). That's one avenue to pursue: assume that for any given cleaner its optimal route will include only those spots closest to it and necessarily exclude spots closer to another cleaner (unless someone can find a counter-example).

So we can divide & conquer the larger graph into n smaller graphs. – AlistairIsrael Oct 28 at 3:05 Easy counterexample re "include only those spots closest to it": n=3 cleaners, on x-axis at x=5,10,15; k=12 spots, at x=1..4,6..9,11..14. – jwpat7 Oct 28 at 18:06.

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.