figure stages of dijkstra' algorithm selection of the vertex is deletemin operationsince once the unknown minimum vertex is foundit is no longer unknown and must be removed from future consideration the update of ' distance can be implemented two ways one way treats the update as decreasekey operation the time to find the minimum is then (log | |)as is the time to perform updateswhich amount to decreasekey operations this gives running time of (|elog | |vlog | | (|elog | |)an improvement