Complete Convergence of Short Paths and Karp's Algorithm for the TSP

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Operations, Information and Decisions Papers
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traveling salesman problem
complete convergence
sub additive processes
subadditive Euclidean functionals
jackknife
Efron-Stein inequality
Other Mathematics
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Steele, John M
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Let Xi, 1 ≤ i < ∞, be uniformly distributed in [0, 1]2 and let Tn be the length of the shortest closed path connecting {X1, X2, …, Xn}. It is proved that there is a constant 0 < β < ∞ such that for all ϵ > 0 ∑n=1∞p(|Tn/n−β‾‾‾‾‾√|>ϵ)<∞.n1∞pTnnβϵ∞ This result is essential in justifying Karp's algorithm for the traveling salesman problem under the independent model, and it settles a question posed by B. W. Weide.

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1981
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Mathematics of Operations Research
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