用广义d-图建模动态规划问题
Modelling dynamic programming problems by generalized d-graphs
摘要：
本文引入广义d-图（容许圈）的概念，作为动态规划（DP）问题建模的特殊依赖图。我们描述了三个著名的单源最短算法（基于顶点拓扑顺序的算法、Dijkstra算法和Bellman-Ford算法）的d-图版本，它们可以被看作是三种不同类型优化问题的一般DP策略。新的建模方法还可以根据图论对DP问题和相应的DP策略进行分类。
英文摘要：
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.
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