关于TSP矩阵“特殊节点”筛选猜想的多项式时间求解潜力及算法价值的技术问询

Hi everyone,

I'm a 19-year-old who's poured 3 years into developing an algorithm focused on pruning symmetric TSP distance matrices, and I’m seeking honest, expert feedback to figure out if this work is worth formalizing and publishing. Here’s a breakdown of what I’ve built, along with my current uncertainty:

Core Algorithm Details #

• Works for both Euclidean and non-Euclidean symmetric TSP
• Can symmetrically remove ~97-98% of edge weights from the original matrix with 100% accuracy: it never eliminates any edge that would be part of the optimal TSP tour
• The pruned matrix only retains edges that are critical to identifying the shortest possible route

Background That Left Me Discouraged #

A year ago, I reached out to Bill Cook (author of The Traveling Salesman Problem: A Computational Study) to share my research. He responded noting he was working on an algorithm that prunes matrices down to ~3n edges (where n = number of nodes), but it only supports Euclidean TSP. While it was exciting to see parallel work in the space, this news crushed my motivation—so much so that I paused refining my algorithm and haven’t shared it with anyone else since.

My Conjecture & Key Questions #

I firmly believe a truly universal TSP solution must handle non-Euclidean cases, as that would make it applicable globally. After analyzing hundreds of printed TSP matrices, I’ve come to suspect this problem has deep connections to number theory. My algorithm is built on a central conjecture that I haven’t yet been able to prove mathematically, but it holds consistently when tested on random TSP matrices.

My main question for this community:

Would an algorithm that can safely prune 97-98% of non-critical edges (with perfect accuracy) for all symmetric TSP cases be considered valuable or novel research?

I’m anxious that I’ve wasted 3 years of work, and I need a reality check to decide whether to polish my research and move forward with publication. Feel free to ask any questions about the conjecture, pruning logic, or test results—I’m happy to elaborate!

备注：内容来源于stack exchange，提问作者Ehsan Javanbakht