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In most of the shortest path problems like vehicle routing problems andnetwork routing problems, we only need an efficient path between two pointssource and destination, and it is not necessary to calculate the shortest pathfrom source to all other nodes. This paper concentrates on this very idea andpresents an algorithm for calculating shortest path for (i) nonnegativeweighted undirected graphs (ii) unweighted undirected graphs. The algorithmcompletes 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 selectionfor that node. The main advantage of the algorithms is its simplicity and itdoes not need complex data structures for implementations.

A O(E) Time Shortest Path Algorithm For Non Negative Weighted Undirected Graphs