We investigate the practical merits of a parallel priority queue through its use in the development of a fast and work-efficient parallel shortest path algorithm, originally designed for an EREW PRAM. Our study reveals that an efficient implementation on a real supercomputer requires considerable effort to reduce the communication performance (which in theory is assumed to take constant time). It turns out that the most crucial part of the implementation is the mapping of the logical processors to the physical processing nodes of the supercomputer. We achieve the requested efficient mapping through a new graph-theoretic result of independent interest: computing a Hamiltonian cycle on a directed hyper-torus. No such algorithm was known before for the case of directed hypertori. Our Hamiltonian cycle algorithm allows us to considerably improve the communication cost and thus the overall performance of our implementation.