The Symmetric Traveling Salesman Problem

Details The Symmetric Traveling Salesman Problem The Symmetric Traveling Salesman Problem

2005-08-11

arxiv.org/abs/math/0508212v3

Mathematics

Combinatorics

A new theorem has been added

Scientific paper

Let M be an nXn symetric matrix, n, even, T, an upper bound for T_OPT, an optimal tour, sigma_T, the smaller-valued perfect matching obtained from alternate edges of T expressed as a product of 2-cycles. Applying the modified Floyd-Warshall algorithm to (sigma_T)^-1M^-, we construct acceptable and 2-circuit cycles some sets of which may yield circuits that can be patched into tours. We obtain necessary and sufficient conditions for a set, S, of cycles to yield circuits that may be patched into a tour.Assume that the following (Condition A)is valid: If (sigma_T)s = T*, |T*|

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