Title Complexity of Layered Binary Search Trees with Relaxed Balance
Authors Lars Jacobsen, University of Southern Denmark
Kim S. Larsen, University of Southern Denmark
Main Fields 6. data types and structures
Other Main Fields
Abstract + Keywords When search trees are made relaxed, balance constraints are weakened such that
updates can be made without immediate rebalancing. This can lead to a
speed-up in some circumstances. However, the weakened balance constraints
also make it more challenging to prove complexity results for relaxed
structures.

In our opinion, one of the simplest and most intuitive presentations of
balanced search trees has been given via layered trees. We show that relaxed
layered trees are among the best of the relaxed structures. More precisely,
rebalancing is worst-case logarithmic and amortized constant per update, and
restructuring is worst-case constant per update.

Keywords: Data Structures, Searchtrees, Relaxed Balance