PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1993-1995 | 22 | 3 | 351-358
Tytuł artykułu

Hamiltonicity and the 3-Opt procedure for the traveling Salesman problem

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The 3-Opt procedure deals with interchanging three edges of a tour with three edges not on that tour. For n≥6, the 3-Interchange Graph is a graph on 1/2(n-1)! vertices, corresponding to the hamiltonian tours in K_n; two vertices are adjacent iff the corresponding hamiltonian tours differ in an interchange of 3 edges; i.e. the tours differ in a single 3-Opt step. It is shown that the 3-Interchange Graph is a hamiltonian subgraph of the Symmetric Traveling Salesman Polytope. Upper bounds are derived for the diameters of the 3-Interchange Graph and the union of the 2- and the 3-Interchange Graphs. Finally, some new adjacency properties for the Asymmetric Traveling Salesman Polytope and the Assignment Polytope are given.
Rocznik
Tom
22
Numer
3
Strony
351-358
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-08-22
Twórcy
  • Department of Econometrics, University of Groningen, The Netherlands
Bibliografia
  • [1] A. Adrabiński and M. M. Sysło, Computational experiments with some approximation algorithms for the travelling salesman problem, Zastos. Mat. 18 (1) (1983), 91-95.
  • [2] M. Grötschel and M. W. Padberg, Polyhedral theory, in: The Traveling Salesman Problem, E. L. Lawler et al. (eds.), Wiley, 1985, 307-360.
  • [3] D. Hausmann, Adjacency in Combinatorial Optimization, Hain, Heisenheim am Glan, 1980.
  • [4] J. K. Lenstra, Sequencing by Enumerative Methods, Math. Center Tracts 69, Amsterdam, 1977.
  • [5] D. Naddef and W. R. Pulleyblank, Hamiltonicity and combinatorial polyhedra, J. Combin. Theory Ser. B 31 (1981), 297-312.
  • [6] D. Naddef and W. R. Pulleyblank, Hamiltonicity in (0-1)-polyhedra, ibid. 37 (1984), 41-52.
  • [7] M. W. Padberg and M. R. Rao, The travelling salesman problem and a class of polyhedra of diameter two, Math. Programming 7 (1974), 32-45.
  • [8] M. R. Rao, Adjacency of the travelling salesman tours and 0-1 vertices, SIAM J. Appl. Math. 30 (1976), 191-198.
  • [9] G. Sierksma, The skeleton of the Symmetric Traveling Salesman Polytope, Discrete Appl. Math. 43 (1993), 63-74.
  • [10] G. Sierksma, Adjacency properties of the Symmetric TSP Polytope, Res. Mem. 464, Inst. of Econ. Res., Univ. of Groningen, 1993.
  • [11] G. Sierksma and G. A. Tijssen, Faces with large diameter on the Symmetric Traveling Salesman Polytope, Oper. Res. Lett. 12 (1992), 73-77.
  • [12] I. Tomescu, Problems in Combinatorics and Graph Theory, Wiley, 1985.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv22z3p351bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.