The R(1)W(1) Communication Model for Self-Stabilizing Distributed Algorithms
Hirotsugu Kakugawa, Sayaka Kamei, Masahiro Shibata, Fukuhito Ooshita
TL;DR
The paper introduces the $R(1)W(1)$ model, which lets a process atomically read and write the local state of its direct neighbors, addressing self-stabilization in distributed systems. It presents self-stabilizing algorithms for three fundamental problems—maximal matching, minimal $k$-dominating set, and maximal $k$-dependent set—under this model, each with linear move complexity and rigorous correctness proofs. A randomized transformer, TrR1W1, converts $R(1)W(1)$ algorithms into a synchronous message-passing implementation with a constant-factor overhead in time and linear in the number of processes for messaging, using distance-two mutual exclusion to simulate the central daemon. The work advances practical fault-tolerant distributed design by bridging abstract models with real-world synchronous systems and outlines future work on extending the approach to $(R(d_r),W(d_w))$ models and more efficient transformers.
Abstract
Self-stabilization is a versatile methodology in the design of fault-tolerant distributed algorithms for transient faults. A self-stabilizing system automatically recovers from any kind and any finite number of transient faults. This property is specifically useful in modern distributed systems with a large number of components. In this paper, we propose a new communication and execution model named the R(1)W(1) model in which each process can read and write its own and neighbors' local variables in a single step. We propose self-stabilizing distributed algorithms in the R(1)W(1) model for the problems of maximal matching, minimal k-dominating set and maximal k-dependent set. Finally, we propose an example transformer, based on randomized distance-two local mutual exclusion, to simulate algorithms designed for the R(1)W(1) model in the synchronous message passing model with synchronized clocks.