Related papers: The consensus number of a shift register equals it…
All consensus hierarchies in the literature assume that we have, in addition to copies of a given object, an unbounded number of registers. But why do we really need these registers? This paper considers what would happen if one attempts to…
The consensus number of an object is the maximum number of processes among which binary consensus can be solved using any number of instances of the object and read-write registers. Herlihy [6] showed in his seminal work that if an object…
We study the ability of different shared object types to solve recoverable consensus using non-volatile shared memory in a system with crashes and recoveries. In particular, we compare the difficulty of solving recoverable consensus to the…
This paper proposes the matrix-weighted consensus algorithm, which is a generalization of the consensus algorithm in the literature. Given a networked dynamical system where the interconnections between agents are weighted by nonnegative…
We describe a linearizable, wait-free implementation of a one-bit swap object from a single max register and an unbounded array of test-and-set bits. Each swap operation takes at most three steps. Using standard randomized constructions,…
Herlihy's wait-free consensus hierarchy classifies the power of object types in asynchronous shared memory systems where processes can permanently crash (i.e. stop taking steps). In this hierarchy, a type has consensus number $n$ if objects…
We consider a quantum circuit in which shift and rotation operations on qubits are performed by swap gates and controlled swap gates. These operations can be useful for quantum computers performing elementary arithmetic operations such as…
Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…
Entry in: Encyclopedia of Algorithms, Ming-Yang Kao, Ed., Springer, To appear. Synonyms: Wait-free registers, wait-free shared variables, asynchronous communication hardware. Problem Definition: Consider a system of asynchronous processes…
String consensus problems aim at finding a string that minimizes some given distance with respect to an input set of strings. In particular, in the Closest string problem, we are given a set of strings of equal length and a radius $d$. The…
This paper introduces the atomic Write and Read Next ($\text{WRN}_{k}$) deterministic shared memory object, that for any $k\ge3$, is stronger than read-write registers, but is unable to implement $2$-processor consensus. In particular, it…
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.…
The objective of this work is to establish a mathematical framework for the study of symmetric shift registers over the field GF(2). The present paper gives a new approach where the symmetric shift registers are represented by associated…
Fault tolerant consensus protocols usually involve ordered rounds of voting between a collection of processes. In this paper, we derive a general specification of fault tolerant asynchronous consensus protocols and present a class of…
The mean shift (MS) is a non-parametric, density-based, iterative algorithm with prominent usage in clustering and image segmentation. A rigorous proof for the convergence of its mode estimate sequence in full generality remains unknown. In…
This work interprets and generalizes consensus-type algorithms as switching dynamics leading to symmetrization of some vector variables with respect to the actions of a finite group. We show how the symmetrization framework we develop…
In this paper, we present an efficient deterministic algorithm for consensus in presence of Byzantine failures. Our algorithm achieves consensus on an $L$-bit value with communication complexity $O(nL + n^4 L^{0.5} + n^6)$ bits, in a…
In this report, building on the deterministic multi-valued one-to-many Byzantine agreement (broadcast) algorithm in our recent technical report [2], we introduce a deterministic multi-valued all-to-all Byzantine agreement algorithm…
Eventually linearizable objects are novel shared memory programming constructs introduced as an analogy to eventual consistency in message-passing systems. However, their behaviors in shared memory systems are so mysterious that very little…
Herlihy's consensus hierarchy ranks the power of various synchronization primitives for solving consensus in a model where asynchronous processes communicate through shared memory and fail by halting. This paper revisits the consensus…