Let N be a network with n nodes and m arcs, and let sigma be the amount of data to be transmitted. The quickest path problem is to find a routing path in N such that the time required to ship sigma units of data from the source to the sink is minimum. The problem considered in this paper is to find the first k quickest simple paths for a given pair of nodes, and an algorithm is designed. The complexity required by the proposed algorithm is O(kmn3 + kmn log k) if the network is directed and is O(kmn2 + kmn log k) if the network is undirected.
