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We prove that the Christofides algorithm gives a approximation ratio for the
special case of traveling salesman problem (TSP) in which the maximum weight in the given
graph is at most twice the minimum weight for the graphs. A
graph is if the number of odd degree vertices in any minimum
spanning tree of the given graph is less than times the number of vertices
in the graph. We prove that the Christofides algorithm is more efficient
(in terms of runtime) than the previous existing algorithms...
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