Distributed and Autonomic Minimum Spanning Trees

TL;DR

This paper introduces an autonomic algorithm for distributed systems to build and maintain scalable, fault-tolerant spanning trees with low degree and depth, supporting efficient broadcast operations.

Contribution

It presents a novel autonomic algorithm that constructs and maintains a dynamic, scalable spanning tree with bounded degree and depth, improving fault tolerance and broadcast efficiency.

Findings

The spanning tree has a maximum depth of log2 n.

Each vertex maintains a degree of exactly log2 n when all processes are correct.

Simulation results show improved scalability and fault tolerance compared to existing methods.

Abstract

The most common strategy for enabling a process in a distributed system to broadcast a message is one-to-all communication. However, this approach is not scalable, as it places a heavy load on the sender. This work presents an autonomic algorithm that enables the $n$ processes in a distributed system to build and maintain a spanning tree connecting themselves. In this context, processes are the vertices of the spanning tree. By definition, a spanning tree connects all processes without forming cycles. The proposed algorithm ensures that every vertex in the spanning tree has both an in-degree and the tree depth of at most $log_2 n$. When all processes are correct, the degree of each process is exactly $log_2 n$. A spanning tree is dynamically created from any source process and is transparently reconstructed as processes fail or recover. Up to $n-1$ processes can fail, and the correct processes remain connected through a scalable, functioning spanning tree. To build and maintain the tree, processes use the VCube virtual topology, which also serves as a failure detector. Two broadcast algorithms based on the autonomic spanning tree algorithm are presented: one for best-effort broadcast and one for reliable broadcast. Simulation results are provided, including comparisons with other alternatives.