Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number (0)
| Venue: | Discrete Appl. Math |
| Citations: | 21 - 14 self |
BibTeX
@ARTICLE{Gutin_polynomialapproximation,
author = {Gregory Gutin and Anders Yeo},
title = {Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number},
journal = {Discrete Appl. Math},
year = {},
volume = {119},
pages = {107--116}
}
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Abstract
Glover and Punnen (1997) asked whether there exists a polynomial time algorithm that always produces a tour which is not worse than at least n!=p(n) tours for some polynomial p(n) for every TSP instance on n cities. They conjectured that, unless P=NP, the answer to this question is negative. We prove that the answer to this question is, in fact, positive. A generalization of the TSP, the quadratic assignment problem, is also considered with respect to the analogous question. Probabilistic, graph-theoretical, group-theoretical and number-theoretical methods and results are used. Key words: Traveling salesman problem, quadratic assignment problem, approximation algorithm. 1 Introduction The domination number, dom(A;n), of an approximation algorithm for the traveling salesman problem (TSP) is the maximum integer k = k(n) such that, for every instance I of the TSP on n cities, A produces a tour T which is not worse than at least k tours in I including T itself. F. Glover and A.P. Punnen...
