ArticleOriginal scientific text
Title
Hamiltonicity and the 3-Opt procedure for the traveling Salesman problem
Authors 1
Affiliations
- Department of Econometrics, University of Groningen, The Netherlands
Abstract
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.
Keywords
Assignment Polytope, Traveling Salesman Polytope
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Pages:
351-358
Main language of publication
English
Received
1993-08-22
Published
1994
Exact and natural sciences