A polynomial-time solution to Papadimitriou and Steiglitz's 'traps'

Authors:
Manfred Padberg;Ting-Yi Sung
Affiliations:
Department of Statistics and Operations Research, Graduate School of Business Administration, New York University, New York, NY 10006, USA;Department of Statistics and Operations Research, Graduate School of Business Administration, New York University, New York, NY 10006, USA
Venue:
Operations Research Letters
Year:
1988

Citing 3
Cited 1

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Abstract

Papadimitriou and Steiglitz constructed 'traps' for the symmetric travelling salesman problem (TSP) with n = 8k cities. The constructed problem instances have exponentially many suboptimal solutions with arbitrarily large weight, which differ from the unique optimal solution in exactly 3k 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.