The Approximation Ratio of the Greedy Algorithm for the Metric Traveling Salesman Problem
We prove that the approximation ratio of the greedy algorithm for the metric Traveling Salesman Problem is $Θ(\log n)$. 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 $Θ(\log n)$.
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