Related papers: Anonymous Obstruction-free $(n,k)$-Set Agreement w…
The $k$-set agreement problem is a generalization of the classical consensus problem in which processes are permitted to output up to $k$ different input values. In a system of $n$ processes, an $m$-obstruction-free solution to the problem…
Determining the space complexity of $x$-obstruction-free $k$-set agreement for $x\leq k$ is an open problem. In $x$-obstruction-free protocols, processes are required to return in executions where at most $x$ processes take steps. The best…
In this article, we investigate the solvability of $k$-set agreement among $n$ processes in distributed systems prone to different types of process failures. Specifically, we explore two scenarios: synchronous message-passing systems prone…
The optimal space complexity of consensus in shared memory is a decades-old open problem. For a system of $n$ processes, no algorithm is known that uses a sublinear number of registers. However, the best known lower bound due to Fich,…
The test-and-set object is a fundamental synchronization primitive for shared memory systems. A test-and-set object stores a bit, initialized to 0, and supports one operation, test&set(), which sets the bit's value to 1 and returns its…
Given a positive integer $k$, $k$-set agreement is the distributed task in which each process $i\in [n]$ in a group of $n$ processing nodes starts with an input value $x_i$ in the set $\{0,\dots,k\}$, and must output a value $y_i$ such that…
The atomic register is certainly the most basic object of computing science. Its implementation on top of an n-process asynchronous message-passing system has received a lot of attention. It has been shown that t \textless{} n/2 (where t is…
This short paper presents a necessary condition for Byzantine $k$-set agreement in (synchronous or asynchronous) message-passing systems and asynchronous shared memory systems where the processes communicate through atomic single-writer…
Nearly thirty years ago, it was shown that $\Omega(\sqrt{n})$ registers are needed to solve obstruction-free consensus among $n$ processes. This lower bound was improved to $n$ registers in 2018, which exactly matches the best upper bound.…
Process anonymity has been studied for a long time. Memory anonymity is more recent. In an anonymous memory system, there is no a priori agreement among the processes on the names of the shared registers they access. This article introduces…
Most algorithms designed for shared-memory distributed systems assume the single-writer multi-reader (SWMR) setting where each process is provided with a unique register readable by all. In a system where computation is performed by a…
Relaxing the sequential specification of a shared object is a way to obtain an implementation with better performance compared to implementing the original specification. We apply this approach to the Counter object, under the assumption…
Despite of being quite similar agreement problems, consensus and general k-set agreement require surprisingly different techniques for proving the impossibility in asynchronous systems with crash failures: Rather than relatively simple…
We consider the minimal k-grouping problem: given a graph G=(V,E) and a constant k, partition G into subgraphs of diameter no greater than k, such that the union of any two subgraphs has diameter greater than k. We give a silent…
This article addresses election in fully anonymous systems made up of $n$ asynchronous processes that communicate through atomic read-write registers or atomic read-modify-write registers. Given an integer $d\in\{1,\dots, n-1\}$, two…
Anonymous shared memory is a memory in which processes use different names for the same shared read/write register. As an example, a shared register named $A$ by a process $p$ and a shared register named $B$ by another process $q$ can…
We consider the task of assigning unique integers to a group of processes in an asynchronous distributed system of a total of $n$ processes prone to crashes that communicate through shared read-write registers. In the Renaming problem, an…
This article presents a signature-free distributed algorithm which builds an atomic read/write shared memory on top of an $n$-process asynchronous message-passing system in which up to $t<n/3$ processes may commit Byzantine failures. From a…
We develop a new lower bound for k-set agreement in synchronous message-passing systems connected by an arbitrary directed communication network, where up to t processes may crash. Our result thus generalizes the t/k+1 lower bound for…
In an anonymous shared memory system, all inter-process communications are via shared objects; however, unlike in standard systems, there is no a priori agreement between processes on the names of shared objects [14,15]. Furthermore, the…