I prove that the average number of comparisons for median-of-k Quicksort (with fat-pivot aka
three-way partitioning) is asymptotically only a constant α k times worse than the lower …

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 …

We characterize the asymptotics of heights of the trees of de la Briandais and the ternary
search trees (TST) of Bentley and Sedgewick. Our proof is based on a new analysis of the …

We introduce a weighted model of random trees and analyze the asymptotic properties of
their heights. Our framework encompasses most trees of logarithmic height that were …

We analyse the weighted height of random tries built from independent strings of iid symbols
on the finite alphabet {1,... d}. The edges receive random weights whose distribution …

In computer science, searching an item or data from a large data set efficiently gives a
challenging task. A search strategy is a procedure that performs many comparisons. It starts …

Abstract We prove the Sedgewick-Bentley conjecture on median-of-k Quicksort on equal
keys: The average number of comparisons for Quicksort with fat-pivot (aka three-way) …