Shortest-path methods: Complexity, interrelations and new propositions

We present a new unified approach for shortest-path problems. Based on this approach, we develop a computational method which consists of determining shortest paths on a finite sequence of partial graphs defined as the “growth of the original graph.” We show that the proposed method allows us to interpret within the same framework several different well-known algorithms, such as those of D′Esopo-Pape, Dijkstra, and Dial, and leads to a uniform analysis of their computational complexity. We also stress the existing parallelism between the proposed method and the matrix-multiplication methods of Floyd-Warshall, and Dantzig.