We present a simple reduction of the problem of nondecreasing paths (with minimal last edge weight) in a directed edge-weighted graph to a reachability problem in a directed unweighted graph. The reduction yields an alternative simple method of solving the single-source nondecreasing paths problem in almost linear time. If the edge weights are integers then our algorithm can be implemented in $O((n+m)\sqrt{\log \log n})$ time on the word RAM, where n and m stand for the number of vertices and edges in the input graph, respectively. By using the reduction, we obtain also a simple algorithm for the all-pairs nondecreasing paths problem. It runs in $\tilde{O}(n^{\omega }\min \{a{w}_G^{\omega },W_G\})$ time, where $a{w}_G$ denotes the average number of distinct weights of edges incident to the same vertex while $W_G$ stands for the total number of distinct edge weights in the input graph G, and ω is the exponent of fast matrix multiplication.

我们将有向边加权图中的非递减路径问题（具有最小的最后边权）简化为有向未加权图中的可达性问题。减少产生了另一种简单的方法，可以在几乎线性的时间内解决单源非递减路径问题。如果边缘权重是整数，那么我们的算法可以在$Ø（（ñ+米）\sqrt{\mathrm{日志}\mathrm{日志}ñ}）$字RAM上的时间，其中n和m分别代表输入图中顶点和边的数量。通过使用约简，我们还获得了用于所有对的非递减路径问题的简单算法。它在$\stackrel{〜}{Ø}（{ñ}^{\omega }\mathrm{分}\{\mathrm{一种}{w}_G^{\omega }，{\mathrm{w\; ^}}_G\}）$ 时间，地点 $\mathrm{一种}{w}_G$ 表示入射到同一顶点的边的不同权重的平均数，而 ${\mathrm{w\; ^}}_G$代表输入图G中不同边缘权重的总数，并且ω是快速矩阵乘法的指数。