Wait-free parallel algorithms for the union-find problem

Abstract

We are interested in designing efficient data structures for a shared memory multiprocessor.In this paper we focus on the union-find data structure. Our machine model is asynchronous and allows stopping faults. 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 been considered by other authors.

Lock-Free Parallel Algorithms: An Experimental Study

“…On the other hand, compare&swap and load-linked, store-conditional have consensus numbers of infinity, hence are universal meaning that they can be used to solve the consensus problem of any number of processes. Lock-free algorithms and protocols have been proposed for many of the commonly used data structures, e.g., linked lists [34], queues [20,25], set [26], union-find sets [2], heaps [6], and binary search trees [33,13]. There were also efforts to improve the performance of lock-free protocols [6,1].…”

Parallelizing Union-Find in Constraint Handling Rules Using Confluence Analysis

“…Parallelization can worsen the performance of optimized union-find, because the find operation is inherently sequential and parallel tree updates can counteract the effects of path compression and union-by-rank [4] so that deep trees (with long paths) are generated. In order to achieve logarithmic worst case time complexity per operation, one has to restrict the parallelism, use special auxiliary data and operations [4] or has to rely on different special-purpose data structures and algorithms altogether [10,5].…”

“…In order to achieve logarithmic worst case time complexity per operation, one has to restrict the parallelism, use special auxiliary data and operations [4] or has to rely on different special-purpose data structures and algorithms altogether [10,5].…”

“…Competing compressions may destroy the tree, even lead to cycles in the tree. These problems are well-known in the literature, different solutions have been proposed like comparing certain counters for nodes or time-stamps, or using a different compression technique like path halving [4]. We prefer a solution that does not introduce additional auxiliary operations or data and that is as close as possible to the original sequential optimal code.…”

“…The bad news is that union-find is inherently sequential in most parts, and therefore hard to parallelize. Its worst case time performance can actually get worse upon parallelization if the sequential algorithm is used as a basis [4]. Often, other data structures and algorithms are used for the parallel union-find problem [10].…”