61 karma · joined February 24, 2021
Most apps are free. The paid one are also already very cheap
I usually go always to the same supermarket twice a week. I was frustrated that every time I changed something in my shopping list I had to mentally recompute the optimal path to pick up everything.
Now with my app I am able to build the graph of the entire supermarket (each node represents a rack with shopping items) and then given my shopping list it computes the optimal path from the entrance to the exit. It's a version of the classical travelling salesman problem
[1]: High-Resolution Image Synthesis With Latent Diffusion Models, https://arxiv.org/abs/2112.10752
A problem A is NP-complete if:
- you can verify it's solution in polynomial time
- you can reduce it to any other NP-complete problem in polynomial time
Since polynomial reduction is transitive, the second point is equivalent to saying that "you can reduce it to SAT in polynomial time".
The reduction is simply a function that compiles the starting problem to SAT and preserves it's solvability (in a bijective way). In other words, to prove that a problem is NP-compelte, you must write a compilation function to SAT and also prove that every solution to the starting problem is also a solution to the destination problem in SAT. Furthermore you must also prove that any solution in the SAT version can be "decompiled" to a proper solution in the starting problem, so this is where the equivalence comes from and it's the reason that SAT is not really anyhow harder than other NP-complete problems.
The thing is, SAT has been heavily researched, so that's why you have extremely efficient SAT-solvers. So if you want to solve an NP-complete problem, you can simply compile it to SAT, solve it with well-known SAT-solvers and "decompile" the solution to your starting problem
what are you referring to?
Obviously x^4 != x^10, but noone has ever proven that "if SAT is P, then it would have the lowest (or highest) polynomial complexity among the other problems", or anything similar
These two words made it all sound like they are just trying to ride the AI wave instead of actually solving a real world problem