Consensus Hierarchy Research Articles

Parsimonious consensus hierarchies, partitions and fuzzy partitioning of a set of hierarchies

Methodology is described for fitting a fuzzy partition and a parsimonious consensus hierarchy (ultrametric matrix) to a set of hierarchies of the same set of objects. A model defining a fuzzy partition of a set of hierarchical classifications, with every class of the partition synthesized by a parsimonious consensus hierarchy is described. Each consensus includes an optimal consensus hard partition of objects and all the hierarchical agglomerative aggregations among the clusters of the consensus partition. The performances of the methodology are illustrated by an extended simulation study and applications to real data. A discussion is provided on the new methodology and some interesting future developments are described.

Separating lock-freedom from wait-freedom at every level of the consensus hierarchy

A long-standing open question has been whether lock-freedom and wait-freedom are fundamentally different progress conditions, namely, can the former be provided in situations where the latter cannot? This paper answers the question in the affirmative, by proving that there are objects with lock-free implementations, but without wait-free implementations—using the same set of objects of any finite coordination power.We precisely define an object called n-process long-lived approximate agreement (n-LLAA), in which two sets of processes associated with two sides, 0 or 1, need to decide on a sequence of increasingly closer outputs. We prove that 2-LLAA has a lock-free linearizable implementation using read/write objects only, and that n-LLAA has a lock-free linearizable implementation using read/write objects and (n−1)-process consensus objects. In contrast, we prove that there is no wait-free linearizable implementation of n-LLAA using read/write objects and specific (n−1)-process consensus objects, called (n−1)-window registers.

Adaptive Active Disturbance Rejection Control for Rendezvous of a Swarm of Drones

This paper addresses the time-varying rendezvous problem of a swarm of drones with the leader-follower consensus hierarchy. Each drone in the swarm is under the influence of external disturbances in the form of wind gusts. To control the swarm of perturbed drones, this paper proposes a fully distributed adaptive leader-following time-varying disturbance rejection pinning control for the rendezvous of drones using the framework of the extended state observer that depends on the state estimates of the neighboring agents rather than the actual states. The communication topology within the swarm is modelled using algebraic graph theory. Unlike most of the literature in which the leader agent act as a virtual reference generator, an active leader agent with non-zero control input is considered. The states of the leader drone are only available to a subset of the graph. The communication topology between leader-follower is directed while that between follower-follower is undirected. Based on the relative output information between the neighboring drones, the extended state observer estimates the local states and disturbances of each drone and the adaptive control actively compensates for the external disturbances simultaneously. Finally, it is shown analytically as well as in simulations that the time-varying rendezvous can be achieved by the proposed algorithm effectively.

Life beyond set agreement

The set agreement power of a shared object O describes O’s ability to solve set agreement problems: it is the sequence $$(n_1, n_2, {\ldots }, n_k, {\ldots })$$ such that, for every $$k\ge 1$$, using O and registers one can solve the k-set agreement problem among at most $$n_k$$ processes. It has been shown that the ability of an object O to implement other objects is not fully characterized by its consensus number (the first component of its set agreement power). This raises the following natural question: is the ability of an object O to implement other objects fully characterized by its set agreement power? We prove that the answer is no: every level $$n \ge 2$$ of Herlihy’s consensus hierarchy has two linearizable objects that have the same set agreement power but are not equivalent, i.e., at least one cannot implement the other. We also show that every level $$n \ge 2$$ of the consensus hierarchy contains a deterministic linearizable object $$O_n$$ with some set agreement power $$(n_1,n_2,\ldots ,n_k,\ldots )$$ such that being able to solve the k-set agreement problems among $$n_k$$ processes, for all $$k\ge 1$$, is not enough to implement $$O_n$$.

A complexity-based classification for multiprocessor synchronization

For many years, Herlihy’s elegant computability-based Consensus Hierarchy has been our best explanation of the relative power of various objects. Since real multiprocessors allow the different instructions they support to be applied to any memory location, it makes sense to consider combining the instructions supported by different objects, rather than considering collections of different objects. Surprisingly, this causes Herlihy’s computability-based hierarchy to collapse. In this paper, we suggest an alternative: a complexity-based classification of the relative power of sets of multiprocessor synchronization instructions, captured by the minimum number of memory locations of unbounded size that are needed to solve obstruction-free consensus when using different sets of instructions.

A Simple Object that Spans the Whole Consensus Hierarchy

This paper presents a simple generalization of the basic atomic read/write register object, whose genericity parameter spans the whole set of integers and is such that its k-parameterized instance has exactly consensus number k. This object, whose definition is natural, is a sliding window register of size k. Its interest lies in its simplicity and its genericity dimension which provides a global view capturing the whole consensus hierarchy. Hence, this short article should be seen as a simple pedagogical introduction to Herlihy’s consensus hierarchy. The paper also shows that the consensus number of a ledger object is [Formula: see text].

On the viability of the deterministic consensus hierarchy

A recent paper by Afek, Ellen, and Gafni introduced a family of deterministic objects Om,k, for m,k≥2, with consensus numbers m such that, for each k≥2, Om,k is computationally less powerful than Om,k+1 in systems with at least mk+m+k processes. This paper gives a wait-free implementation of Om,k from (m+1)-consensus objects and registers in systems with finitely many processes. In order to do so, it introduces a new family of objects which helps us to understand the power of m-consensus in a system with more than m processes.

B-cell Ligand Processing Pathways Detected by Large-scale Comparative Analysis

The initiation of B-cell ligand recognition is a critical step for the generation of an immune response against foreign bodies. We sought to identify the biochemical pathways involved in the B-cell ligand recognition cascade and sets of ligands that trigger similar immunological responses. We utilized several comparative approaches to analyze the gene coexpression networks generated from a set of microarray experiments spanning 33 different ligands. First, we compared the degree distributions of the generated networks. Second, we utilized a pairwise network alignment algorithm, BiNA, to align the networks based on the hubs in the networks. Third, we aligned the networks based on a set of KEGG pathways. We summarized our results by constructing a consensus hierarchy of pathways that are involved in B cell ligand recognition. The resulting pathways were further validated through literature for their common physiological responses. Collectively, the results based on our comparative analyses of degree distributions, alignment of hubs, and alignment based on KEGG pathways provide a basis for molecular characterization of the immune response states of B-cells and demonstrate the power of comparative approaches (e.g., gene coexpression network alignment algorithms) in elucidating biochemical pathways involved in complex signaling events in cells.

The Travelling Citizen: Emergent Discourses of Moral Mobility in a Study of Cycling in London

Drawing on accounts of travelling within London, this article explores the ways in which mobility discourses are tied to the responsibilities of ‘a good citizen’ and suggests that car-dominated automobility has been significantly fractured, at least in one urban setting. A consensus hierarchy of transport modes now configures driving as immoral, as well as dysfunctional, and cycling, in contrast, as particularly laudable. Within this new moral economy of transport, cycling holds the promise of conscientious automobility, enabling a number of explicit and implied citizenship responsibilities to be met. These include ecological responsibilities to the city and global ecosystem, but also responsibilities to enact the ‘new citizen’: a knowledgeable and alert risk-assessor competent to travel in ways that maximize independence, efficiency and health. However, cycling has its own contradictions: whilst enabling some to enact a new ‘moral’ citizenship, it simultaneously underlines the marginal citizenship of less mobile Londoners.

Quantifying the RR of harm to self and others from substance misuse: results from a survey of clinical experts across Scotland

ObjectiveTo produce an expert consensus hierarchy of harm to self and others from legal and illegal substance use.DesignStructured questionnaire with nine scored categories of harm for 19 different commonly used...

All of Us Are Smarter than Any of Us: Nondeterministic Wait-Free Hierarchies Are Not Robust

A wait-free hierarchy ACM Transactions on Programming Languages and Systems, 11 (1991), pp. 124--149; Proceedings of the 12th ACM Symposium on Principles of Distributed Computing, 1993, pp. 145--158] classifies object types on the basis of their strength in supporting wait-free implementations of other types. Such a hierarchy is robust if it is impossible to implement objects of types that it classifies as "strong" by combining objects of types that it classifies as "weak." We prove that if nondeterministic types are allowed, the only wait-free hierarchy that is robust is the trivial one, which lumps all types into a single level. In particular, the consensus hierarchy (the most closely studied wait-free hierarchy) is not robust. Our result implies that, in general, it is not possible to determine the power of a concurrent system that supports a given set of primitive object types by reasoning about the power of each primitive type in isolation.

Determining Consensus Numbers

Conditions on a shared object type T are given that are both necessary and sufficient for wait-free n-process consensus to be solvable using objects of type T and registers. The conditions apply to two large classes of deterministic shared objects: read-modify-write objects [C. P. Kruskal, L. Rudolph, and M. Snir, { ACM Trans. Prog. Lang. Syst., 10 (1988), pp. 579--601] and readable objects, which have operations that allow processes to read the state of the object. These classes include most objects that are used as the primitives of distributed systems. When the sequential specification of T is finite, the conditions may be checked in a finite amount of time to decide the question "Is the consensus number of T at least n?" The conditions are also used to provide a clear proof of the robustness of the consensus hierarchy for read-modify-write and readable objects.

Preserving consensus hierarchies

In numerical taxonomy we often have the task of finding a consensus hierarchy for a given set of hierarchies. This consensus hierarchy should reflect the substructures which are common to all hierarchies of the set. Because there are several kinds of substructures in a hierarchy, the general axiom to preserve common substructures leads to different axioms for each kind of substructure. In this paper we consider the three substructurescluster, separation, andnesting, and we give several characterizations of hierarchies preserving these substructures. These characterizations facilitate interpretation of axioms for preserving substructures and the examination of properties of consensus methods. Finally some extensions concerning the preserving of qualified substructures are discussed.