The space requirement of m-ary search trees: distributional asymptotics for m >= 27

Abstract

We study the space requirement of $m$-ary search trees under the random permutation model when $m \geq 27$ is fixed. Chauvin and Pouyanne have shown recently that $X_n$, the space requirement of an $m$-ary search tree on $n$ keys, equals $\mu (n+1) + 2\Re{[\Lambda n^{\lambda_2}]} + \epsilon_n n^{\Re{\lambda_2}}$, where $\mu$ and $\lambda_2$ are certain constants, $\Lambda$ is a complex-valued random variable, and $\epsilon_n \to 0$ a.s. and in $L^2$ as $n \to \infty$. Using the contraction method, we identify the distribution of $\Lambda$.