A Bound of 4 for the Diameter of the Symmetric Traveling Salesman Polytope
نویسندگان
چکیده
We investigate the diameter of the polytope arising in the n-city symmetric traveling salesman problem (TSP) and perfect matching polytopes. Grötschel and Padberg [The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, Wiley-Intersci. Ser. Discrete Math., E. Lawler et al., eds., John Wiley, Chichester, 1985, pp. 251–305] conjectured that the diameter of the symmetric TSP polytope is 2, independent of n. We constructively show that its diameter is at most 4, for all n ≥ 3. Our result also shows that the diameter of the perfect 2-matching polytope is at most 6, for every n ≥ 3.
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ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 11 شماره
صفحات -
تاریخ انتشار 1998