Algorithm for Finding Second Critical Path by Safety Float

This paper addresses a simple and fast algorithm for finding the second critical path in CPM network by safety float. The algorithm is based on the properties of safety float and the relationship between the length of a path and its safety float. The paper argues that the longest path passing through the activity immediately succeeding the critical node with the minimum non-zero safety float is the second critical path, and then the algorithm is presented and proved to be correct. Complexity analysis shows that the algorithm runs in O(m) time, where m is the number of arcs in the network.