The Approximation Ratio of the Greedy Algorithm for the Metric Traveling Salesman Problem

Abstract

We prove that the approximation ratio of the greedy algorithm for the metric Traveling Salesman Problem is $\Theta (\log n)$. Moreover, we prove that the same result also holds for graphic, Euclidean, and rectilinear instances of the Traveling Salesman Problem. Finally we show that the approximation ratio of the Clarke-Wright savings heuristic for the metric Traveling Salesman Problem is $\Theta (\log n)$.