The recently-proposed generic Dijkstra algorithm finds shortest paths in networks with continuous and contiguous resources. While the algorithm was proposed in the context of optical networks (and is applicable to other networks with finite and discrete resources), we present the stated problem in a broader algorithmic setting of the greedy approach. 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 greedy approach and the Bellman principle of optimality to algebraic structures with a partial ordering. By analyzing the size of the search space in the worst-case, we argue the stated problem is tractable. Thus we definitely answer a long-standing fundamental question of whether we can efficiently find a shortest path in a network with discrete resources subject to the continuity and contiguity constraints: yes, we can.

翻译：最近提出的通用Dijkstra算法能够在具有连续且相邻资源的网络中找到最短路径。虽然该算法是在光网络背景下提出的（并适用于其他具有有限离散资源的网络），但我们将所述问题置于更广泛的贪心算法框架中进行阐述。原算法发表时未提供正确性证明，且存在微小缺陷。我们补全了缺失的证明，并对缺陷进行了修正。为证明算法正确性，我们将贪心策略和贝尔曼最优性原理推广到具有偏序关系的代数结构。通过分析最坏情况下搜索空间的规模，我们论证了所述问题是可处理的。因此，我们明确回答了一个长期存在的根本性问题：能否在满足连续性和相邻性约束条件下，高效地找到具有离散资源网络中的最短路径？答案是肯定的。