Open Access

Pedro Maristany de las Casas, Antonio Sedeno-Noda, Ralf Borndörfer

• We present a new label-setting algorithm for the Multiobjective Shortest Path (MOSP) problem that computes a minimum complete set of efficient paths for a given instance. The size of the priority queue used in the algorithm is bounded by the number of nodes in the input graph and extracted labels are guaranteed to be efficient. These properties allow us to give a tight output-sensitive running time bound for the new algorithm that can almost be expressed in terms of the running time of Dijkstra’s algorithm for the Shortest Path problem. Hence, we suggest to call the algorithm Multiobjective Dijkstra Algorithm (MDA). The simplified label management in the MDA allows us to parallelize some subroutines. In our computational experiments, we compare the MDA and the classical label-setting MOSP algorithm by Martins, which we improved using new data structures and pruning techniques. On average, the MDA is 2 to 9 times faster on all used graph types. On some instances the speedup reaches an order of magnitude.