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Approximation Algorithms for the Traveling Salesman Problem with Range Condition
Published online by Cambridge University Press: 15 April 2002
Abstract
We prove that the Christofides algorithm gives a $\frac{4}{3}$ 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 odd degree restricted graphs. A
graph is odd degree restricted if the number of odd degree vertices in any minimum
spanning tree of the given graph is less than $\frac{1}{4}$
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 for this special case of the
traveling salesman problem. Secondly, we apply the concept of stability of approximation
to this special case of traveling salesman problem in order to partition the set of all
instances of TSP into an infinite spectrum of classes according to their approximability.
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- Research Article
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- © EDP Sciences, 2000
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