Polynomial Algorithms for the Tsp and the Qap with a Factorial Domination Number
نویسندگان
چکیده
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.
منابع مشابه
Dominance guarantees for above-average solutions
Gutin et al. [G. Gutin, A. Yeo, Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number, Discrete Applied Mathematics 119 (1–2) (2002) 107–116] proved that, in the ATSP problem, a tour of weight not exceeding the weight of an average tour is of dominance ratio at least 1/(n − 1) for all n 6= 6. (Tours with this property can be easily obtained.) In [N. Alon...
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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 quadra...
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