On the Optimality and Speed of the Deep Greedy Switching Algorithm for Linear Assignment Problems

The Deep Greedy Switching algorithm is a fast heuristic for solving large instances of the linear sum assignment problem whilst sacrificing very little in terms of optimality. In this paper we explore the worst case performance aspects of the algorithm. We prove that the algorithm is finite and analyze its computational complexity. We also discuss a number of simplified variations of the algorithm that shed some light on how the algorithm works. The basic algorithm is also extended to problems involving partial assignment. Computational results on a number of problem types show that the solutions reached by our algorithm are only slightly worse than those obtained by the auction algorithm. A parallelized version of the basic algorithm is presented. Our algorithm is significantly faster than other methods with approaching a comparable quality of solution.