Neighborhood Mutual Remainder:Self-Stabilizing Distributed Implementationand Applications

Abstract

This paper considers a situation where each process has a set of operations Op and executes each operation in Op infinitely often in distributed systems. Then, let Oe ⊂ Op be a subset of operations, which cannot be executed by a process while its closed neighborhood execute operations in Op∖ Oe. For such a situation, this new concept of Neighborhood Mutual Remainder (NMR) is defined. 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∖ Oe. We formalize the concept of NMR and give a simple self-stabilizing algorithm to demonstrate the design paradigm to achieve NMR. We present an application of NMR to a LOOK-COMPUTE-MOVE (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 implementations of the LCM synchronization for environments where each robot can have limited visibility and lights.