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Approximation Algorithms for the Traveling Salesman Problem with Range Condition

D. Arun KumarC. Pandu Rangan — 2010

RAIRO - Theoretical Informatics and Applications

We prove that the Christofides algorithm gives a 4 3 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 1 4 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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