Abstract
Papadimitriou and Steiglitz constructed ‘traps’ for the symmetric travelling salesman problem (TSP) with n = 8 k cities. The constructed problem instances have exponentially many suboptimal solutions with arbitrarily large weight, which differ from the unique optimal solution in exactly 3 k edges, and hence local search algorithms are ineffective to solve this problem. However, we show that this class of ‘catastrophic’ examples can be solved by linear programming relaxation appended with k subtour elimination constraints. It follows that this class of problem instances of TSP can be optimized in polynomial time.
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