Shortest path and related problems have been a very hot topic for researchers since Dijekstra devised his first shortest path algorithm. In transportation and communication routing, during the execution of system, failure of any link needs robust and most effective recovery. In such problems we need some recovery mechanism and/or plan for the continuation of the process with minimum or no delay with least, additional, recovery cost. This paper presents initial finding and achievements to recover from a single link failure on the shortest path with optimal alternate path keeping the cost low. ©2010 IEEE.