The recently-proposed generic Dijkstra algorithm finds shortest paths in networks with continuous and contiguous resources. The algorithm was proposed in the context of optical networks, but is applicable to networks with finite and discrete resources. The algorithm was published without a proof of correctness, and with a minor shortcoming. We provide that missing proof and offer a correction to the shortcoming. To prove the algorithm correct, we generalize the Bellman's principle of optimality to algebraic structures with a partial ordering. We also argue the stated problem is tractable by analyzing the size of the search space in the worst-case.

翻译：近期提出的通用Dijkstra算法用于在具有连续且邻接资源的网络中寻找最短路径。该算法最初在光网络背景下提出，但同样适用于有限离散资源网络。原算法发表时未提供正确性证明，且存在细微缺陷。我们补全了这一缺失的证明，并对该缺陷进行了修正。为证明算法的正确性，我们将贝尔曼最优性原理推广至具有偏序关系的代数结构。同时，通过分析最坏情况下搜索空间的规模，论证了所述问题的可解性。