A GPU Parallel Algorithm for Finding a Negative Subset Disjoint Cycle in a Graph

Many problems in combinatorial optimization rely on local search heuristics attempting to swap elements between subsets. The best results are achieved by combining multiple exchanges, where the multi-subset move can be described as a subset disjoint cycle. Finding a valid cycle becomes the core part of the search routine, and the valid cycle of minimum weight corresponds to the best possible move. The problem complexity has been growing at a rapid pace in recent years, hitting the limits of both exact and heuristic approaches. We propose a parallel algorithm for finding subset disjoint negative cycles of minimum weight and a GPU accelerated implementation. The approach is exact if the memory limit is sufficient and heuristic otherwise. A parallel hashmap structure is provided to meet the specific needs of the algorithm. The computational experiments demonstrate up to 60x speedup with respect to the sequential alternative. We showcase the practical benefits of our algorithm for a time sensitive variant of the vehicle routing problem.