Quantitative relaxation of concurrent data structures

Abstract

There is a trade-off between performance and correctness in implementing concurrent data structures. Better performance may be achieved at the expense of relaxing correctness, by redefining the semantics of data structures. We address such a redefinition of data structure semantics and present a systematic and formal framework for obtaining new data structures by quantitatively relaxing existing ones. We view a data structure as a sequential specification containing all "legal" sequences over an alphabet of method calls. Relaxing the data structure corresponds to defining a distance from any sequence over the alphabet to the sequential specification: the k-relaxed sequential specification contains all sequences over the alphabet within distance k from the original specification. In contrast to other existing work, our relaxations are semantic (distance in terms of data structure states). As an instantiation of our framework, we present two simple yet generic relaxation schemes, called out-of-order and stuttering relaxation, along with several ways of computing distances. We show that the out-of-order relaxation, when further instantiated to stacks, queues, and priority queues, amounts to tolerating bounded out-of-order behavior, which cannot be captured by a purely syntactic relaxation (distance in terms of sequence manipulation, e.g. edit distance). We give concurrent implementations of relaxed data structures and demonstrate that bounded relaxations provide the means for trading correctness for performance in a controlled way. The relaxations are monotonic, which further highlights the trade-off: increasing k increases the number of permitted sequences, which as we demonstrate can lead to better performance. Finally, since a relaxed stack or queue also implements a pool, we obtain new concurrent pool implementations that outperform the state-of-the-art ones.

Verifying a quantitative relaxation of linearizability via refinement

“…Despite the advantages of quasi linearizability and its rising popularity (e.g., [9,12,17]), such relaxed consistency property is difficult to test and verify. Inspit of being an important property of concurrent data structures, there does not yet exist any effective way of formally verifying this relaxed correctness condition.…”

“…Realizing that a more relaxed correctness condition than linearizability suffices in many applications, Afek et al [1] have defined a new notion called quasi linearizability. Quasi linearizability is a quantitative relaxation of linearizability [9,12,17] to allow for more flexibility in how the data structures are implemented. While preserving the basic intuition of linearizability, quasi linearizability relaxes the semantics of the data structures to achieve increased runtime performance.…”

The lock-free k-LSM relaxed priority queue

“…Quasi linearizability has been used as a consistency condition for FIFO queues [1,5], but is not restricted to these. Later work by Henzinger et al [10] provided a closely related model called quantitative relaxation.…”

The SprayList: a scalable relaxed priority queue

“…Recently, there has been a surge of interest in relaxed concurrent data structures, both on the theoretical side, e.g. [15] and from practitioners, e.g. [22].…”

“…Our work can be seen as part of a broader research direction on high-throughput concurrent data structures with relaxed semantics [15,26]. Examples include container data structures which (partially or entirely) forgo ordering semantics such as the rendezvous mechanism [2] or the CAFE task pool [4].…”