I was wondering something, let's say in a symmetric distance matrix of a sample of TSP, there was a sure algorithm that could remove around 97% of the values (weights or distances) that wouldn't definitely be used in order to get the shortest routes in the end, would such algorithm be valuable and something new? For example, we have a TSP system, let's make a square matrix with the distances between the nodes, obviously there's one shortest path for example but we don't know it, my algorithm will remove (symmetrically since the values on the other side of them matrix are the same) 98% of the weights that aren't needed in order to make the shortest route in the end and it's 100% accurate meaning that it will never remove a "good weight" that's needed to be used to make the shortest path in the end. I've been working on this for 3 years now, I have a very long interesting research to publish that I think will definitively be a starting path to solve tis problem. My algorithm is based on my main hypothesis and I just want to see if I wasted 3 years of my life (I'm 19) for absolutely nothing I just need some confidence to see if I should publish it or not. BTW, my algorithm works for both euclidean and non-euclidean TSP. The document I uploaded here is a letter sent to Bill Cook (the person who wrote The Traveling Salesman Problem: A Computational Study) a year ago and I received response that he was also working on an algorithm that apparently reduced the weights to 3n where n is the number of nodes but only worked for euclidean TSP, which is absolutely amazing and at the same time, it devastated me and made me more depressed than I was, so I never showed it to anyone else and didn't really continue perfecting it, I believe a true solution to TSP should be non-euclidean, hence it would be global, and with the amount of experience I gained by looking at hundreds of printed TSP matrices, I can tell that this problem is very close to a number theory problem, and I still believe my conjecture that I unfortunately can't yet prove mathematically is the path towards the ultimate solution, you can try it yourself right now, make a random TSP matrix and try my conjecture. Any insights about this would be very appreciated. I apologize if I didn't sound professional or like a PhD guy. If you had any questions, I'd be happy to answer. Thanks guys!
Here's the file with more explanation: https://docs.google.com/document/d/1EpoB2uS_QnEaweDEIOl2ucLaHrd4QD5EJfxh8ww9fwM/edit?usp=sharing
Here are my results: https://docs.google.com/spreadsheets/d/1sW5cf5lUIc5l87EwoXnuJy7tOY7SLHud/edit?usp=sharing&ouid=117626413598749411847&rtpof=true&sd=true
Nope. It likely doesn't hold promise. Polynomial time is about asymptotic running time. Constant factors are irrelevant. An algorithm that takes $2^m$ time to handle $m$ edges is exponential; an algorithm that first removes 99% of the edges, then runs the prior method, will take $2^{0.01m}$ time, which is also exponential.