On the equivalence between some shortest path algorithms

Abstract

In this paper, we show the equivalence between a particular implementation of the Partitioned Shortest Path (PSP) algorithm, Moore's algorithm, and a dynamic programming approach with an appropriate state space and decision space reduction, when applied to a problem of determining a shortest simple path from a given node to all the nodes in a network having arbitrary costs but with no negative cost circuits. This equivalence provides insights into the PSP method, shows that Moore's algorithm has a polynomial-time implementation, and facilitates by definition the proofs of various properties.