Time Complexity of Distributed Topological Self-stabilization: The Case of Graph Linearization

Topological self-stabilization is an important concept to build robust open distributed systems (such as peer-to-peer systems) where nodes can organize themselves into meaningful network topologies. The goal is to devise distributed algorithms that converge quickly to such a desirable topology, independently of the initial network state. This paper proposes a new model to study the parallel convergence time. Our model sheds light on the achievable parallelism by avoiding bottlenecks of existing models that can yield a distorted picture. As a case study, we consider local graph linearization—i.e., how to build a sorted list of the nodes of a connected graph in a distributed and self-stabilizing manner. We propose two variants of a simple algorithm, and provide an extensive formal analysis of their worst-case and best-case parallel time complexities, as well as their performance under a greedy selection of the actions to be executed.

• Type: Conference
• Year: 2010
• Where: LATIN
• Authors: Dominik Gall, Riko Jacob, Andréa W. Richa, Christian Scheideler, Stefan Schmid, Hanjo Täubig
• Keywords: Information Retrieval, LATIN 2010, Meaningful Network Topologies, Open Distributed Systems, Parallel Convergence Time