A concurrent van Emde Boas array as a fast and simple concurrent dynamic set alternative

Abstract

SUMMARYIncreasing demand for computationally efficient algorithms and processors has turned the attention of researchers toward parallel and concurrent solutions. Because the frequency of contemporary processors cannot be tweaked infinitely, the only hopes for squeezing more performance from computers are parallel processing and parallel computation. The important part of every parallel solution is concurrent data structures, which allow multithread programming environments to be taken advantage of. In this article, a new concurrent dynamic set structure is proposed. It is based on the van Emde Boas trees concept, where on every node of a tree, an array of the node's children is stored. The structure is equipped with a simple but effective locking algorithm, which allows it to be used concurrently by any number of threads. The presented algorithm idea is accompanied by an experimental implementation written in JAVA 6. Preliminary tests prove that, especially for moderately larger data sets with a predominance of read operations, the concurrent van Emde Boas array proposed in this article may be a viable alternative for other structures providing a similar functionality.

Dynamic concurrent van Emde Boas array

“…The next method get(), similarly to insert(), first retrieves the current snapshot of the dcvEB array parameters (Listing: 5, Line: 60), then traverses the structure down from the root to the leaf following the subsequent level positions. The main difference between get() in the dcvEB array and get() from the previous version of the structure [15] is that currently the enabled bit in a summary does not guarantee the existence of the corresponding lower level array holder. Hence, the additional check whether the next AH is not actually nil is necessary (Listing: 5, Lines: 67 -68).…”

“…The second and the major subroutine of delete() is delIntern(). In terms of the synchronization structure, it is similar to the original delete() method presented in [15]. The need, however, for effective array holder removal caused the necessity to introduce a few new elements into the code of the algorithm.…”

“…For example, in the vEB tree, the delete() method performs one single pass from the top to bottom. Due to synchronization issues in the dcvEB array [15] the delete() method proceeds bottom-up. Similarly, successor() and predecessor() first reach the bottom of the tree, then start to traverse the tree moving up and down in search of the appropriate element.…”

“…The dcvEB and cvEB arrays can be seen as a tree of arrays [15]. Each array's cell holds the reference to ArrayHolder (AH) -a tree node structure, which wraps the lower-level array or stores a specific value if AH is a leaf.…”

“…Such a situation makes the search for new concurrent data structures particularly important. One of the attempts to find such a structure is the work [15] in which the author proposed the early version of the concurrent van Emde Boas (cvEB ) array. The structure presented here is an example of concurrent dynamic set implementation providing, in addition to the standard methods insert(), remove() and find(), also the method successor(), which allows users to determine the first greater element from the specified one.…”