Details

Autor(en) / Beteiligte

• Broutin, N.
• Devroye, L.
• McLeish, E.

Titel

Weighted height of random trees

Ist Teil von

• Acta informatica, 2008-06, Vol.45 (4), p.237-277

Ort / Verlag

Berlin/Heidelberg: Springer-Verlag

Erscheinungsjahr

2008

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We consider a model of random trees similar to the split trees of Devroye (SIAM J. Comput. 28(2), 409–432, 1998) in which a set of items is recursively partitioned. Our model allows for more flexibility in the choice of the partitioning procedure, and has weighted edges. We prove that for this model, the height H n of a random tree is asymptotic to c log n in probability for a constant c that is uniquely characterized in terms of multivariate large deviations rate functions. This extension permits us to obtain the height of pebbled tries, pebbled ternary search tries, d -ary pyramids, and to study geometric properties of partitions generated by k -d trees. The model also includes all polynomial families of increasing trees recently studied by Broutin et al. (The height of increasing trees. Random Structures and Algorithms, 2007, in press).