Let N be a network with n nodes and m arcs, and let σ 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 σ 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)nlogn+k3’/2logk) is developed.
