%0 Journal Article %T The Moments of the Profile in Random Binary Digital Trees %A Kazemi, Ramin %A Delavar, Saeid %J Journal of Mathematics and Computer Science %D 2013 %V 6 %N 3 %@ ISSN 2008-949X %F Kazemi2013 %X The purpose of this paper is to provide a precise analysis of the \(t\)-th moment of the profile in random binary digital trees. We assume that the \(n\) input strings are independent and follow a (binary) Bernoulli model. In tries, the main difference with the previous analysis is that we have to deal with an inhomogeneous part in the proper functional equation satisfied by the \(t\)-th moment and in digital search trees with an inhomogeneous part in a proper functional-differential equation. We show that \(t\)-th moment of the profile (\(t\geq 2\)) is asymptotically of the same order as the expected value (\(t=1\)). These results are derived by methods of analytic combinatorics. %9 journal article %R 10.22436/jmcs.06.03.02 %U http://dx.doi.org/10.22436/jmcs.06.03.02 %P 176-190 %0 Journal Article %T Distribution of inter-node distances in digital trees %A R. Cguech %A K. Lasmar %A H. M. Mahmoud %J International Conference on Cnalysis of Clgorithms, DMTCS proc. CD %D 2005 %V %F Cguech2005 %0 Journal Article %T File searching using variable length keys %A R. de la. Briandais %J Proceedings of the AFIPS Spring Joint Computer Conference. AFIPS Press, Reston, Va. %D 1959 %V %F Briandais1959 %0 Journal Article %T File structures using hashing functions %A J. E. CoGman %A T. Eve %J Communications of the ACM %D 1970 %V 13 %F CoGman1970