Parallel Label-Setting Multi-objective Shortest Path Search

We present a parallel algorithm for finding all Pareto optimal paths from a specified source in a graph. The algorithm is label-setting, i.e., it only performs work on distance labels that are optimal. The main result is that the added complexity when going from one to multiple objectives is completely parallelizable. The algorithm is based on a multiobjective generalization of a priority queue. Such a Pareto queue can be efficiently implemented for two dimensions. Surprisingly, the parallel biobjective approach yields an algorithm performing asymptotically less work than the previous sequential algorithms. We also discuss generalizations for d ≥ 3 objective functions and for single target search.