Upper and Lower Bounds for Deterministic Approximate Objects

Abstract

Relaxing the sequential specification of shared objects has been proposed as a promising approach to obtain implementations with better complexity. In this paper, we study the step complexity of relaxed variants of two common shared objects: max registers and counters. In particular, we consider the k-multiplicative-accurate max register and the k-multiplicativeaccurate counter, where read operations are allowed to err by a multiplicative factor of k (for some k ∈ N). More accurately, reads are allowed to return an approximate value x of the maximum value v previously written to the max register, or of the number v of increments previously applied to the counter, respectively, such that v/k ≤ x ≤ v • k. We provide upper and lower bounds on the complexity of implementing these objects in a wait-free manner in the shared memory model.