Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number

نویسندگان

  • Gregory Gutin
  • Anders Yeo
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.

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عنوان ژورنال:
  • Discrete Applied Mathematics

دوره 119  شماره 

صفحات  -

تاریخ انتشار 2002