Wait-free Parallel Algorithms for the Union-Find Problem

We are interested in designing efficient data structures for a shared memory multiprocessor. In this paper we focus on the Union-Find data structure. We consider a fully asynchronous model of computation where arbitrary delays are possible. Thus we require our solutions to the data structure problem have the wait-free property, meaning that each thread continues to make progress on its operations, independent of the speeds of the other threads. In this model efficiency is best measured in terms of the total number of instructions used to perform a sequence of data structure operations, the work performed by the processors. We give a wait-free implementation of an efficient algorithm for Union-Find. In addition we show that the worst case performance of the algorithm can be improved by simulating a synchronized algorithm, or by simulating a larger machine if the data structure requests support sufficient parallelism. Our solutions apply to a much more general adversary model than has be..