Generalized Traveling Salesman Problem Reduction Algorithms - Gutin, Gregory; Karapetyan, Daniel (Algorithmic Operations Research, 2009)
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 optimal solution. The algorithm’s running time is O(N3) 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 10–60% for each of the considered solvers.