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The travelling salesman problem (TSP) is an NP-hard problem in combinatorial optimization studied in operations research and theoretical computer science. Given a list of cities and their pairwise distances, the task is to find a shortest possible tour that visits each city exactly once.
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Cheapest Insertion is $2$-approximation for TSP
I know that this is a $2$ approximation to the Metric Travelling Salesman Problem (TSP), but I am wondering how we could prove that this is actually the case. …