source to the vertex and additional preprocessing of vertices is used to achieve faster implementations [@boland_dethridge_dumitrescu; @desrochers_desrosiers_solomon]. The ideas of first passage percolation and label correction have naturally appeared in the design of [*pulse algorithms*]{} for constrained shortest paths [@lozano_medaglia]. All of the mentioned algorithms can also be parallelized but this task would require a different approach in designing a memory management that would handle the label sets in programming environments where dynamical data structures need to be avoided.

The method of aggressive edge elimination [@muhandiramge_boland] can be parallelized to solve the Lagrange dual problems. In the case of road and railroad networks a substantial speedup can be achieved by using a preprocessing of the network data and applying a generalized versions of Dijkstra’s algorithm [@kohler_mohring_schilling].

The parallel algorithm that is most similar in nature to the one discussed in this paper is developed for wireless networks [@li_wan_wang_frieder]. There are two features of wireless networks that are not available to our model. The first feature is that the communication time between the vertices can be assumed to be constant. The other feature is that wireless networks have a processing element available to each vertex. Namely, routers are usually equipped with 