An Approximate Algorithm for Triangle TSP with a Four-Vertex-Three-Line Inequality

Traveling salesman problem (TSP) is a classic combinatorial optimization problem. The time complexity of the exact algorithms is generally an exponential function of the scale of TSP. This work gives an approximate algorithm with a four-vertex-three-line inequality for the triangle TSP. The time complexity is O(n2) and it can generate an approximation less than 2 times of the optimal solution. The paper designs a simple algorithm with the inequality. The algorithm is compared with the double-nearest neighbor algorithm. The experimental results illustrate the algorithm find the better approximations than the double-nearest neighbor algorithm for most TSP instances.

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