I'm reading Efficient Shortest Path Simplex Algorithms by Donald Goldfarb, Jianxiu Hao and Shen-Roan Kai who considered "the specialization of the primal simplex algorithm to the problem of finding a tree of directed shortest paths from a given node to all other nodes in a network of n nodes or finding a directed cycle of negative length. Two efficient variants of this shortest path simplex algorithm are analyzed and shown to require at most $(n − 1)(n − 2)/2$ pivots and $O(n^3)$ time."
I'm trying to find motivation for this article and wonder isn't Bellman-Ford algorithm good enough? It works in $O(nm)$ time which and good for the type of graph which the problem above algorithm deals with.