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 looping paths from the source to the sink, and an algorithm with time complexity of O(m2 + (m + k)n log n + k3/2 log k) is developed.
