B-slack trees: Highly Space Efficient B-trees

TL;DR

B-slack trees are a space-efficient subclass of B-trees that optimize worst-case space complexity while maintaining efficient update times, with a version suitable for concurrent environments.

Contribution

Introduction of B-slack trees with improved worst-case space complexity and an accompanying relaxed version for concurrent implementation.

Findings

Store n keys in height O(log_b n)

Update operations in O(log_{b/2} n) amortized time

Relaxed version suitable for concurrent systems

Abstract

B-slack trees, a subclass of B-trees that have substantially better worst-case space complexity, are introduced. They store $n$ keys in height $O(\log_b n)$, where $b$ is the maximum node degree. Updates can be performed in $O(\log_{\frac b 2} n)$ amortized time. A relaxed balance version, which is well suited for concurrent implementation, is also presented.