At-Most-Once Semantics in Asynchronous Shared Memory

At-most-once semantics is one of the standard models for object access in decentralized systems. Accessing an object, such as altering the state of the object by means of direct access, method invocation, or remote procedure call, with at-most-once semantics guarantees that the access is not repeated more-than-once, enabling one to reason about the safety properties of the object. This paper investigates implementations of at-most-once access semantics in a model where a set of such actions is to be performed by a set of failure-prone, asynchronous shared-memory processes. We introduce a definition of the at-most-once problem for performing a set of n jobs using m processors and we introduce a notion of efficiency for such protocols, called effectiveness, used to classify algorithms. Effectiveness measures the number of jobs safely completed by an implementation, as a function of the overall number of jobs n, the number of participating processes m, and the number of process crashes f in the presence of an adversary. We prove a lower bound of n - f on the effectiveness of any algorithm. We then prove that this lower bound can be matched in the two process setting by presenting two algorithms that offer a tradeoff between time and space complexity. Finally, we generalize our two-process solution in the multi-process setting with a hierarchical algorithm that achieves effectiveness of n - logmċo(n), coming reasonably close, asymptotically, to the corresponding lower bound.