Average Complexity of Additive Properties for Multiway Tries: A Unified Approach (Extended Abstract)

We study multiway asymmetric tries. Our main interest is to investigate the depth of a leaf and the external path length, however we also formulate and solve a more general problem. We consider a class of properties called additive properties. This class is specified by a common recurrence relation. We give an exact solution of the recurrence, and present an asymptotic approximation. In particular, we derive all (factorial) moments of the depth of a leaf and the external path length. In addition, we solve an open problem of Paige and Tarjan about the average case complexity of the improved lexicographical sorting. These results extend previous analyses by Knuth [12], Flajolet and Sedgewick [6], Jacquet and Regnier [10], and Kirschenhofer and Prodinger [11].