The distribution of m-ary search trees generated by van der Corput sequences

Wolfgang Steiner (1)

1 Institut für Geometrie

We study the structure of $m$-ary search trees generated by the van der Corput sequences. The height of the tree is calculated and a generating function approach shows that the distribution of the depths of the nodes is asymptotically normal. Additionally a local limit theorem is derived.

Mots clés: arbre de recherche m-aire; suite de van der Corput; théorème central limite; série génératrice

Domaines: Mathématique discrète [cs.DM]

Wolfgang Steiner. The distribution of m-ary search trees generated by van der Corput sequences. Discrete Mathematics and Theoretical Computer Science, 2004, 6 (2), pp.409-424. ⟨hal-00023232v2⟩