- finds an approximate solution for [[Traveling Sales Problem Optimization Version (TSP-OPT)]] - given the graph $G = (V, E)$ compute its [[Minimum Spanning Trees (MST)]] - run $DFS$ on that $MST$, record vertices visited - i.e ABCDCECBA - return unique vertices in pre-order as tour, skipping any repeated vertices - ABCDE - but first vertex must be appended at end, so real answer is **ABCDEA** - runtime of $O(n\,log(n))$ - when $G$ satisfies the triangle inequality, this algorithm achieves an approximation factor of 2