In the search for optimal concurrency

It is common practice to use the epithet “highly concurrent” referring to data structures that are supposed to perform well in concurrent environments. But how do we measure the concurrency of a data structure in the first place? In this paper, we propose a way to do this, which allowed us to formalize the notion of a concurrency-optimal implementation. The concurrency of a program is defined here as the program’s ability to accept concurrent schedules, i.e., interleavings of steps of its sequential implementation. To make the definition sound, we introduce a novel correctness criterion, LS-linearizability, that, in addition to classical linearizability, requires the interleavings of memory accesses to be locally indistinguishable from sequential executions. An implementation is then concurrency-optimal if it accepts all LS-linearizable schedules.We explore the concurrency properties of search data structures which can be represented in the form of directed acyclic graphs exporting insert, delete and search operations. We prove, for the first time, that pessimistic (e.g., based on conservative locking) and optimistic serializable (e.g., based on serializable transactional memory) implementations of search datastructures are incomparable in terms of concurrency. Thus, neither of these two implementation classes is concurrency-optimal, hence raising the question of the existence of concurrency-optimal programs.