A Probabilistic Analysis of Christofides' Algorithm
Abstract: Christofides’ algorithm is a well known approximation algorithm for the metric travelling salesman problem. As a first step towards obtaining an average case analysis of Christofides’ algorithm, we provide a probabilistic analysis for the stochastic version of the algorithm for the Euclidean traveling salesman problem, where the input consists of n randomly chosen points in [0,1]d. Our main result provides bounds for the length of the computed tour that hold almost surely. We also provide an experimental evaluation of Christofides’s algorithm.
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