The height of Mallows trees
Louigi Addario-Berry, Beno\^it Corsini

TL;DR
This paper investigates the height of binary search trees built from Mallows permutations, revealing different asymptotic behaviors depending on the parameter q and the relation between n and log n.
Contribution
It extends the understanding of binary search tree heights to Mallows permutations, identifying three regimes of asymptotic behavior based on the parameter q and the size n.
Findings
For q in [0,1], the height asymptotically behaves as (1+o(1))(c* log n + n(1-q)).
Three regimes of height behavior depending on the limit of n(1-q)/log n.
When n(1-q)/log n tends to zero, height is of order c* log n, similar to uniform case.
Abstract
Random binary search trees are obtained by recursively inserting the elements of a uniformly random permutation of into a binary search tree data structure. Devroye (1986) proved that the height of such trees is asymptotically of order , where is the unique solution of with . In this paper, we study the structure of binary search trees built from Mallows permutations. A permutation is a random permutation of whose probability is proportional to , where . This model generalizes random binary search trees, since permutations with are uniformly distributed. The laws of and are…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
