Asynchronous Self-stabilization Made Fast, Simple, and Energy-efficient
Pages 538 - 548
Abstract
Distributed systems are ubiquitous, and their distributed nature make them particularly vulnerable to faults. Being able to automatically recover from these faults is of utmost importance, and self-stabilization is a general and lightweight approach to tackle this problem. However, fully asynchronous self-stabilizing algorithms (FASS) are notoriously difficult to design and prove. It thus makes sense to create and prove a transformer that turns synchronous algorithms into FASSes.
The Rollback Compiler of Awerbuch and Varghese (FOCS 1991) is such a transformer. The problem is that although it produces FASSes that are fast (time being evaluated in rounds), we prove that their energy requirement (measured through the number of state changes) can be exponential in the number n of nodes. Actually, regardless of the problem, the literature only contains a few FASSes which are asymptotically optimal time-wise. Moreover, several of these algorithms have been shown to require an exponential amount of energy, and no such algorithms are known to be energy-efficient.
In this paper, we introduce the first transformer that turns any terminating synchronous algorithm into a fully asynchronous self-stabilizing algorithm with essentially the same time complexity and with a low energy requirement (polynomial in n). However, as for the rollback compiler, this comes at the cost of a (reasonable) memory increase. Our approach is compatible with most models, ranging from the LOCAL model (a powerful synchronous fault-free model), down to models such as the Stone Age model, in which a node cannot even know how many neighbors it has.
In particular, we can transform extremely fast algorithms such as the classical Θ{log*n)-time ring coloring algorithm by Cole and Vishkin (FOCS 1986) into fast and energy-efficient FASSes. We also provide the best FASSes so far for many classical distributed problems such as leader election and spanning tree constructions (e.g., BFS, shortest-path).
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Index Terms
- Asynchronous Self-stabilization Made Fast, Simple, and Energy-efficient
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Published In
June 2024
570 pages
ISBN:9798400706684
DOI:10.1145/3662158
- Chair:
- Ran Gelles,
- Proceedings Chair:
- Dennis Olivetti,
- Program Chair:
- Petr Kuznetsov
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Published: 17 June 2024
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