Neighborhood mutual remainder: self-stabilizing distributed implementation and applications

Abstract

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 \(O_p\) and executes each operation in \(O_p\) infinitely often in distributed systems. Then, let \(O_e\subset O_p\) be a subset of operations, which a process cannot execute, while its closed neighborhood executes operations in \(O_p\setminus O_e\). 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 \(O_p\) infinitely often and (2) safety is satisfied if, when each process executes operations in \(O_e\), no process in its closed neighborhood executes operations in \(O_p\setminus O_e\). 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 transient 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 system 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.