Neighborhood mutual remainder: self-stabilizing distributed implementation and applications

Dolev Shlomi

Kamei Sayaka

Katayama Yoshiaki

Ooshita Fukuhito

Wada Koichi

Acta Informatica

Motivated by the need to convert move-atomic assumption in LOOK-COMPUTE-MOVE (LCM) robot algorithms to be implemented in existing distributed systems, we define a new distributed fundamental task, the Neighborhood Mutual Remainder (NMR). Consider a situation where each process has a set of operations Op and executes each opera-tion in Op infinitely often in distributed systems. Then, let Oe ⊂ Op be a subset of operations, which a process cannot execute while its closed neighborhood executes operations in Op n Oe. The NMR is defined for such a situation. A distributed algorithm that satisfies the NMR requirement should satisfy the following two properties: (1) Liveness is satisfied if a process executes each operation in Op infinitely often, and (2) safety is satisfied if, when each process executes operations in Oe, no process in its closed neighborhood executes operations in Op n Oe. We formalize the concept of NMR and give a simple self-stabilizing algorithm using the pigeon-hole principle to demonstrate the design paradigm to achieve NMR. A self-stabilizing algorithm tolerates tran-sient faults (e.g., message loss, memory corruption, etc.) by its ability to converge from an arbitrary configuration to the legitimate one. In addition, we present an application of NMR to an LCM robot sys-tem for implementing a move-atomic property, where robots possess an independent clock that is advanced at the same speed. It is the first self-stabilizing implementation of the LCM synchronization for environments where each robot can have limited visibility and lights.

eng

Springer

This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00236-023-00450-8

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[DOI] https://doi.org/10.1007/s00236-023-00450-8 isVersionOf