Complexity of Layered Binary Search Trees with Relaxed Balance

Lars Jacobsen, Kim Skak Larsen

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review


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.
Original languageEnglish
Title of host publicationTheoretical Computer Science, 7th Italian Conference, ICTCS 2001
Number of pages16
Publication date2001
Publication statusPublished - 2001
EventSeventh Italian Conference on Theoretical Computer Science - Torino, Italy
Duration: 4. Oct 20016. Oct 2001


ConferenceSeventh Italian Conference on Theoretical Computer Science
SeriesLecture Notes in Computer Science


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