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Neighborhood Mutual Remainder: Self-Stabilizing Implementation of Look-Compute-Move Robots (Extended Abstract)
Local mutual exclusion guarantees that no two neighboring processes enter a
critical section at the same time while satisfying both mutual exclusion and no
starvation properties. On the other hand, processes may want to execute some
operation simultaneously with the neighbors. Of course, we can use a globally
synchronized clock to achieve the task but it is very expensive to realize it
in a distributed system in general.
In this paper, we define a new concept neighborhood mutual remainder. A
distributed algorithm that satisfies the neighborhood mutual remainder
requirement should satisfy global fairness, l-exclusion and repeated local
rendezvous requirements. Global fairness is satisfied when each process (that
requests to enter the critical section infinitely often) executes the critical
section infinitely often, l-exclusion is satisfied when at most l neighboring
processes enter the critical section at the same time, and repeated local
rendezvous is satisfied when for each process infinitely often no process in
the closed neighborhood is in the critical or trying section.
We first formalize the concept of neighborhood mutual remainder, and give a
simple self-stabilizing algorithm to demonstrate the design paradigm to achieve
neighborhood mutual remainder. We also present two applications of neighborhood
mutual remainder to a Look-Compute-Move robot system. One is for implementing a
move-atomic property and the other is for implementing FSYNC scheduler, where
robots possess an independent clock that is advanced in the same speed. These
are the first self-stabilizing implementations of the LCM synchronization.Comment: 16 page