Generalized Traveling Salesman Problem Reduction Algorithms
Gregory Gutin and D. Karapetyan
Algoithmic Operations Research
The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The aim of this paper is to present a problem reduction algorithm that deletes redundant vertices and edges, preserving the value of the optimal solution. The algorithm's running time is $O(N^3)$ in the worst case, but it is significantly faster in practice. The algorithm has reduced the problem size by 15--20\% on average in our experiments and this has decreased the solution time by approximately 45\% for each of the three solvers considered.