扩展Dijkstra算法与Moore-Bellman-Ford算法
Extended Dijkstra algorithm and Moore-Bellman-Ford algorithm
AI总结：
本文定义路径函数，提出一般单源最短路径问题，并设计扩展Dijkstra算法和扩展Moore-Bellman-Ford算法，分别以O(n^2)M(n)和O(mn)M(n)时间求解，通过实例展示应用，推动最短路径理论的研究与应用。
摘要：
研究一般单源最短路径问题。首先，在图上的具有相同源点的一些路径集合上定义路径函数，并针对所定义的路径函数发展一类一般单源最短路径问题（GSSSP）。其次，分别遵循著名的Dijkstra算法和Moore-Bellman-Ford算法的思路，设计扩展Dijkstra算法（EDA）和扩展Moore-Bellman-Ford算法（EMBFA），以在给定条件下求解GSSSP问题。第三，引入若干概念，如路径函数的末路保序性（OPLR）等。在假设任意路径的相关路径函数值可在M(n)时间内获得的条件下，分别证明算法EDA在O(n^2)M(n)时间内求解GSSSP问题，算法EMBFA在O(mn)M(n)时间内求解GSSSP问题。最后，通过若干例子展示所设计算法的应用。我们的工作可促进最短路径理论的研究与应用。
英文摘要：
Study the general single-source shortest path problem. Firstly, define a path function on a set of some path with same source on a graph, and develop a kind of general single-source shortest path problem (GSSSP) on the defined path function. Secondly, following respectively the approaches of the well known Dijkstra's algorithm and Moore-Bellman-Ford algorithm, design an extended Dijkstra's algorithm (EDA) and an extended Moore-Bellman-Ford algorithm (EMBFA) to solve the problem GSSSP under certain given conditions. Thirdly, introduce a few concepts, such as order-preserving in last road (OPLR) of path function, and so on. And under the assumption that the value of related path function for any path can be obtained in $M(n)$ time, prove respectively the algorithm EDA solving the problem GSSSP in $O(n^2)M(n)$ time and the algorithm EMBFA solving the problem GSSSP in $O(mn)M(n)$ time. Finally, some applications of the designed algorithms are shown with a few examples. What we done can improve both the researchers and the applications of the shortest path theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
