Self-stabilizing Balancing Algorithm for Containment-Based Trees

Abstract

Abstract-Containment-based trees encompass various handy structures such as B+-trees, R-trees and M-trees. They are widely used to build data indexes, range-queryable overlays, publish/subscribe systems both in centralized and distributed contexts. In addition to their versatility, their balanced shape ensures an overall satisfactory performance. Recently, it has been shown that their distributed implementations can be faultresilient. However, this robustness is achieved at the cost of unbalancing the structure. While the structure remains correct in terms of searchability, its performance can be significantly decreased. In this paper, we propose a distributed self-stabilizing algorithm to balance containment-based trees.

Maintaining balanced trees for structured distributed streaming systems

“…Some work has also been done in the context of Peer-to-Peer networks such as [14] that proposes a self-stabilizing algorithm for computing spanning tree in large scale systems where any pair of processes can communicate directly under condition of knowing receiver's identifier. The work closest to ours is the one in [3] that proposes a self-stabilizing algorithm that builds a balanced-tree (in the context of containment trees).…”

“…Therefore, our algorithm is not strictly self-stabilizing. However, under this relaxation, we are able to precisely analyze the time complexity of our algorithms which was not done in previous work (in particular in [3]).…”