To Solve problems such as how to seek any k-th order path in CPM network in project scheduling,some new conceptions: The k-th order normal activity,the k-th order eigenvalue and the k-th order normal path,are given.The free float theorem and eigenvalue theorem are deduced by analyzing these conceptions and the characteristics of free float.Then,an algorithm of seeking the k-th order critical path—the smallest eigenvalue algorithm whose complexity is O(n2),is proposed according to these conceptio...