Abstract
We suggest a polynomial-time approximation algorithm for the traveling salesman problem which is based on a randomized version of an algorithm for the assignment problem. The probabilistic analysis of the algorithm is performed in the case of a random distance matrix whose columns form a sequence of symmetrically dependent random variables. Under some additional assumptions on the value of the scatter coefficient of the distance matrix entries we prove that the algorithm is asymptotically optimal and establish the corresponding estimates for the relative error and fault probability.
This research was partially supported by the Russian Foundation for Fundamental Research (Grant 93–01–00417).
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© 1996 Kluwer Academic Publishers
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Gimadi, È.K., Glebov, N.I., Serdyukov, A.I. (1996). An Approximation Algorithm for the Traveling Salesman Problem and Its Probabilistic Analysis. In: Korshunov, A.D. (eds) Discrete Analysis and Operations Research. Mathematics and Its Applications, vol 355. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1606-7_4
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DOI: https://doi.org/10.1007/978-94-009-1606-7_4
Publisher Name: Springer, Dordrecht
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