Shortest Paths In Euclidean Graphs
Robert Sedgewick, Jeffrey Scott Vitter · 2005
We analyze a simple method for finding shortest paths in Euclidean graphs (where vertices are points in a Euclidean space and edge weights are distances between points). For many graph models, the running time of the algorithm to find the shortest path between a specified pair of vertices in a graph with V vertices and E edges is shown to be O(V) as compared with O (V log V + E) required by the classical (Dijkstra) algorithm.