Machine Learning for Two-Stage Graph Sparsification for the Travelling Salesman Problem

ArXi:2604.20236v1 Announce Type: new High-performance TSP solvers like LKH search within a sparsified candidate graph rather than over all possible edges. Graph sparsification is non-trivial: keep too many edges and the solver wastes time; cut too many and it loses edges that belong to the optimal tour. The two leading heuristic methods, $\alpha$-Nearest and POPMUSIC, produce high-quality candidate graphs, but no single heuristic is both sparse and reliable across all instance sizes and distributions. Machine learning methods can potentially learn better sparsification models.