An Experimental Evaluation and Investigation of Waves of Misery in R-trees

TL;DR

This paper investigates waves of misery in R-trees, revealing their impact on performance, and proposes techniques like regular and unequal splits to mitigate these effects, improving index stability during insertions.

Contribution

It is the first comprehensive study of waves of misery in R-trees and introduces novel techniques to reduce their impact on performance.

Findings

Linear and Quadratic R-trees are more resilient to waves of misery.

Regular Elective Splits (RES) can reduce performance variability.

Unequal Random Splits (URS) offer an alternative mitigation method.

Abstract

Waves of misery is a phenomenon where spikes of many node splits occur over short periods of time in tree indexes. Waves of misery negatively affect the performance of tree indexes in insertion-heavy workloads.Waves of misery have been first observed in the context of the B-tree, where these waves cause unpredictable index performance. In particular, the performance of search and index-update operations deteriorate when a wave of misery takes place, but is more predictable between the waves. This paper investigates the presence or lack of waves of misery in several R-tree variants, and studies the extent of which these waves impact the performance of each variant. Interestingly, although having poorer query performance, the Linear and Quadratic R-trees are found to be more resilient to waves of misery than both the Hilbert and R*-trees. This paper presents several techniques to reduce the impact in performance of the waves of misery for the Hilbert and R*-trees. One way to eliminate waves of misery is to force node splits to take place at regular times before nodes become full to achieve deterministic performance. The other way is that upon splitting a node, do not split it evenly but rather at different node utilization factors. This allows leaf nodes not to fill at the same pace. We study the impact of two new techniques to mitigate waves of misery after the tree index has been constructed, namely Regular Elective Splits (RES, for short) and Unequal Random Splits (URS, for short). Our experimental investigation highlights the trade-offs in performance of the introduced techniques and the pros and cons of each technique.