Deletion without Rebalancing in Multiway Search Trees

Many database systems that use a B+ tree as the underlying data structure do not do rebalancing on deletion. This means that a bad sequence of deletions can create a very unbalanced tree. Yet such databases perform well in practice. Avoidance of rebalancing on deletion has been justified empirically and by average-case analysis, but to our knowledge no worst-case analysis has been done. We do such an analysis. We show that the tree height remains logarithmic in the number of insertions, independent of the number of deletions. Furthermore the amortized time for an insertion or deletion, excluding the search time, is O(1), and nodes are modified by insertions and deletions with a frequency that is exponentially small in their height. The latter results do not hold for standard B+ trees. By adding periodic rebuilding of the tree, we obtain a data structure that is theoretically superior to standard B+ trees in many ways. We conclude that rebalancing on deletion can be considered harmful...

• Type: Conference
• Year: 2009
• Where: ISAAC
• Authors: Siddhartha Sen, Robert Endre Tarjan
• Keywords: Algorithms, B+ Trees, ISAAC 2009, Rebalancing, Standard B+ Trees