  In this paper we introduce the concept of generalized d-graph (admitting
cycles) as special dependency-graphs for modelling dynamic programming (DP)
problems. We describe the d-graph versions of three famous single-source
shortest algorithms (The algorithm based on the topological order of the
vertices, Dijkstra algorithm and Bellman-Ford algorithm), which can be viewed
as general DP strategies in the case of three different class of optimization
problems. The new modelling method also makes possible to classify DP problems
and the corresponding DP strategies in term of graph theory.
