Splitting and Renaming with a Majority of Faulty Processes

Abstract

Splitters are simple objects, implementable with read/write registers, that return directions in {right, down, stop}. Not every process that accesses the object obtains the same direction, and in addition at most one obtains stop. Both in their one-shot and long-lived form, splitters are basic building block of elegant renaming algorithms in shared memory. In a message passing system when less than half of the processes may fail, splitter can be implemented by first simulating shared registers. This is no longer the case if half or more of the processes may fail. We define and implement one-shot and long-lived splitters suited to the majority of failures environment. Our generalized splitters retain most properties of the original splitters, except that they only guarantee that at most ⌊ n/n − f) ⌋ processes return stop, where n is the number of processes and f < n an upper bound on the number of failures. We then adapt Moir and Anderson grid of splitters to solve one-shot and long-lived variant of renaming in which at most ⌊ n/n − f) ⌋ processes may obtain the same name. One of the main challenge consists in composing long-lived generalized splitters.