What is Fully Dynamic All-Pairs Shortest Path Algorithm

The topic of shortest path algorithms is very fundamental and important in information science and technology. Shortest path algorithms have evolved over many years and have found applications in different domains such as telecommunication networks, military, and transportation. There has been a lot of work undertaken on this topic in this area in the past. A lot of research is still being conducted. The topic is still poorly understood. This article should be helpful to readers, because it reviews some of the important works conducted in the area, out of the plenty of works available on this topic. The problem is so fundamental that whatever the interest areas of the readers may be, they will find the article useful. The popular traditional shortest path algorithms date back to 1958/1959 and were proposed by Dijkstra (1959), and Bellman (1958). Their algorithms found wide applications in the abovementioned domains for many years. However, they were static. Thereafter, many other algorithms were proposed in the last few decades, all of which can be classified to be either dynamic or semi-dynamic.