A O(|E|) Time Shortest Path Algorithm for Non-Negative Weighted Undirected Graphs

In most of the shortest path problems like vehicle
routing problems and network routing problems, we only need
an efficient path between two points—source and destination,
and it is not necessary to calculate the shortest path from source
to all other nodes. This paper concentrates on this very idea and
presents an algorithms for calculating shortest path for (i) nonnegative
weighted undirected graphs (ii) unweighted undirected
graphs. The algorithm completes its execution in O(|E|) for all
graphs except few in which longer path (in terms of number of
edges) from source to some node makes it best selection for that
node.