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≥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
μ(n+1)+2R[Λ
n
λ
2
]+
ϵ
n
n
R
λ
2
, where
μ
and
λ
2
are certain constants,
Λ
is a complex-valued random variable, and
ϵ
n
→0
a.s. and in
L
2
as
n→∞
. Using the contraction method, we identify the distribution of
Λ
.