B-slack trees: Highly Space Efficient B-trees

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.