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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 $k$-multiplicative-accurate counter, where read operations are allowed to err by a multiplicative factor of $k$ (for some $k in mathbb{N}$). 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 $v/k leq x leq v cdot k$. We provide upper and lower bounds on the complexity of implementing these objects in a wait-free manner in the shared memory model.
In this paper, we study the lower- and upper-bounded covering (LUC) problem, where we are given a set $P$ of $n$ points, a collection $mathcal{B}$ of balls, and parameters $L$ and $U$. The goal is to find a minimum-sized subset $mathcal{B}subseteq ma
The emergence of systems with non-volatile main memory (NVM) increases the interest in the design of emph{recoverable concurrent objects} that are robust to crash-failures, since their operations are able to recover from such failures by using state
We prove a query complexity lower bound for $mathsf{QMA}$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $mathsf{SBP}^A otsubset mathsf{QMA}^A$, resolving
Given a graph $G = (V,E)$, an $(alpha, beta)$-ruling set is a subset $S subseteq V$ such that the distance between any two vertices in $S$ is at least $alpha$, and the distance between any vertex in $V$ and the closest vertex in $S$ is at most $beta$
A recent sequence of works, initially motivated by the study of the nonlocal properties of entanglement, demonstrate that a source of information-theoretically certified randomness can be constructed based only on two simple assumptions: the prior ex