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On Quorum Systems for Group Resources with Bounded Capacity
Abstract
We present a problem called (m,1,k)-resource allocation to model group mutual exclusion with bounded capacity. Specifically, the problem concerns the scheduling of a resource among
m groups of processes. The resource can be used by at most k processes of the same group at a time, but no two processes of different groups can use the resource simultaneously. The
problem reduces to group mutual exclusion when k is equal to the group size. We then generalize quorum systems for mutual exclusion to the problem. We show that the study
of quorum systems for (m,1,k)-resource allocation is closely related to some classical problems in combinatorics and in finite projective geometries.
By applying the results there, we are able to obtain some optimal/near-optimal quorum systems.
... Moreover, taking a purely mathematical perspective, we think that group quorum systems are an elegant object which study is well justified. Group quorum systems of optimal degree are described in [10]. Unfortunately, the work in [10] requires n to be of the form x 2 , where x is a power of a prime. ...
... Group quorum systems of optimal degree are described in [10]. Unfortunately, the work in [10] requires n to be of the form x 2 , where x is a power of a prime. This is the case because the proposed system in [10] is derived from an affine plane of order x and it is known that such an affine plane exists if x is a power of a prime. ...
... Unfortunately, the work in [10] requires n to be of the form x 2 , where x is a power of a prime. This is the case because the proposed system in [10] is derived from an affine plane of order x and it is known that such an affine plane exists if x is a power of a prime. ...
The group mutual exclusion problem is a generalization of the ordinary mutual exclusion problem where each applica-tion process can be a member of different groups and mem-bers of the same group are allowed simultaneous access to their critical sections. Members of different groups must access their critical sections in a mutually exclusive man-ner. Quorum-based solutions have been proposed for solv-ing the mutual exclusion problem in both settings. Recently, there has been a growing interest in designing group quorum systems for group mutual exclusion. The disadvantage of this approach is that it limits the level of concurrency (also known as degree) of any m-group quorum system (m > 1) to √ n, where n is the number of manager processes in the system. The advantage is that it provides a way from which truly distributed quorum-based solutions for group mutual exclusion can be easily constructed. Group quorum sys-tems of optimal degree are known only for n = p 2k , where p is a prime, and k is a positive integer. The best known group quorum system that works for any n and m > 1 is due to Joung (2003) and has degree k = Õ 2n m(m−1) . In this paper, we describe a new group quorum system of degree k ′ = 1 + Ô 1 + n m , which is much higher than k for m > 3. Also when k ′ = k, our system produces quorums of smaller size for m > k/2.
... Recently, Lawi and Yamashita [16], and Joung [11] independently introduced and defined (m, h, k)-resource allocation as a general conflict resolution problem which relaxes the safety requirement of the k-mutex and GME problems. The problem models the above resource allocation problems and designs a conflict resolution such that the following two requirements are satisfied: at any given time at most h (out of m) resources can be utilized by some users simultaneously , and each resource is utilized by at most k concurrent users at a time. ...
... However, their algorithm may not allow users to utilize h resources and hence the degree of concurrency may not reach hk. Another quorum system, called (m, 1, k)-coterie, has also been introduced by Joung [11], but it can only solve the problem for h = 1. This paper presents a quorum based algorithm for (m, h, k)-resource allocation problem. ...
... The properties of (m, h, k)-coterie follow properties of (extended) k-coteries in which a pair of intersecting and non-intersecting quorums are associated with a bicoterie and a disjoint pair of coteries , respectively. It would also be easy to observe that the (m, 1, k)-coterie introduced in Joung [11] is just one example of (m, h, k)-coteries when h = 1. Some intuitive examples of the new quorum system are also presented. ...
In this paper, we present a quorum based algorithm for (m, h, k)-resource allocation problem, i.e., a con- flict resolution problem to control a distributed sys- tem consisting of n users and m critical resources so that the following two requirements are satisfied: at any given time, at most h (out of m) resources can be utilized by some users simultaneously and each re- source is utilized by at most k concurrent users. The problem is a natural generalization of several well- studied conflict resolution problems such as mutual exclusion, k-mutual exclusion, generalized mutual exclusion and group mutual exclusion. The (m, h, k)- resource allocation problem can be solved by employ- ing a k-mutual exclusion algorithm, however, it is in- efficient in terms of the message complexity. We thus propose a new algorithm and a new quorum system (m, h, k)-coterie used in it. Then we show that all re- quirements of the problem are guaranteed, and the maximum degree hk of concurrency is achieved as de- sired and the message complexity is the same as for a single k-coterie based algorithm.
... The distributed k-mutual exclusion problem is the problem of managing processes in a distributed system in such a way that at most k processes can enter their critical sections simultaneously. Several distributed k-mutual exclusion algorithms have been proposed [2,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. ...
... Since the nondominated coteries are the most resilient, it is beneficial to find as general as possible an algorithm to constructing k-coteries. Some researchers have observed and analyzed the advantages of using nondominated coteries, such as [1,16,17,20,21]. ...
p> One of the solution in solving k mutual exclusion problem is the concept of k-coterie. A k-coterie under a set S is a set of subsets of S or quorums such that any k + 1 quorums, there are at least two quorums intersect each other. The k mutual exclusion problern is the problem of managing processes in such a way that at most k processes can enter their critical sections simultaneously. Nondominated k-coteries are more resilient to network and site failures than doninated k-coteries; that is the availability and reliability of a distributed system is better if nondominated k-coteries are used. Algorithms to construct k-coteries have been proposed, unfortunately they have some restrictions, especially in constructing nondominated k-coteries. The restrictions are due to the combination of N, the number of nodes in a distributed system, and k, the number of processes allowed to enter their critical sections simultaneously. To solve this problem, this paper proposes an algorithm to construct nondominated k-coteries for all combination of N and k. </p
... Furthermore, the idea of developing the concept of bicoterie was born into a set system with more than two elements. In 2004, [4] introduced the -coteri quorum system, but was limited to . Finally [5] succeeded in answering the limitations of by the discovery of a new set systems called coterie. ...
Quorum system of ( h, k )-majority coterie is a set system which elements are a collection of sets k -coterie provided that each element satisfies bicoterie and disjoint properties. Some of related studies have tried to make the construction of this quorum system but constrained by the problem of generalization. In this paper, to overcome the problem we first compile an equation to determine the size of quoru m. Then we arrange quoru ms that satisfies the equation in a quorum system. The way are (a) divide the universe set into m parts so that h parts are separated, (b) construct a quorum that satisfie k -coterie, (c) construct a quorum system that satisfie bicoterie and disjoint properties.
... De ce fait, la notion de plusieurs sections a été introduite. Le même auteur a posé le problème d'allocation de ressources (m, 1, k) pour modéliser l'exclusion mutuelle de groupes à capacité bornée, dans laquelle une ressource donnée peut être utilisée au plus par simultanément k processus du même groupe [Jou04]. ...
Data Handover est une librairie de fonctions adaptée aux systèmes distribués à grande échelle. Dho offre des routines qui permettent d'acquérir des ressources en lecture ou en écriture de façon cohérente et transparente pour l'utilisateur. Nous avons modélisé le cycle de vie de Dho par un automate d'état fini puis, constaté expérimentalement, que notre approche produit un recouvrement entre le calcul de l'application et le contrôle de la donnée. Les expériences ont été menées en mode simulé en utilisant la libraire GRAS de SimGrid puis, en exploitant un environnement réel sur la plate-forme Grid'5000. Par la théorie des files d'attente, la stabilité du modèle a été démontrée dans un contexte centralisé. L'algorithme distribué d'exclusion mutuelle de Naimi et Tréhel a été enrichi pour offrir les fonctionnalités suivantes: (1) Permettre la connexion et la déconnexion des processus (ADEMLE), (2) admettre les locks partagés (AEMLEP) et enfin (3) associer les deux propriétés dans un algorithme récapitulatif (ADEMLEP). Les propriétés de sûreté et de vivacité ont été démontrées théoriquement. Le système peer-to-peer proposé combine nos algorithmes étendus et le modèle originel Dho. Les gestionnaires de verrou et de ressource opèrent et interagissent mutuellement dans une architecture à trois niveaux. Suite à l'étude expérimentale du système sous-jacent menée sur Grid'5000, et des résultats obtenus, nous avons démontré la performance et la stabilité du modèle Dho face à une multitude de paramètres
... De ce fait, la notion de plusieurs sections a été introduite. Le même auteur a posé le problème d'allocation de ressources (m, 1, k) pour modéliser l'exclusion mutuelle de groupes à capacité bornée, dans laquelle une ressource donnée peut être utilisée au plus par simultanément k processus du même groupe [Jou04]. ...
Data handover, Dho is a library of functions adapted to large-scale distributed systems. It provides routines that allow to acquire resources in reading or writing in the ways that are coherent and transparent for users. We modeled the life cycle of Dho by a finite state automaton and through experiments, we have found that our approach produced an overlap between the calculation of the application and the controle of the data. These experiments were conducted both in simulated mode and in real environment (within Grid'5000). We exploited the GRAS library of the SimGrid toolkit. Several clients try to access the resource concurrently according the client-server paradigm. By the theory of queues, the stability of the model was demonstrated in a centralized environment. We improved, the distributed algorithm for mutual exclusion (of Naimi and Trehel), by introducing following features: (1) Allowing the mobility of processes (ADEMLE), (2) introducing shared locks (AEMLEP) and finally (3) merging both properties cited above into an algorithm summarising (ADEMLEP). We proved the properties, Safety and liveliness, theoretically for all extended algorithms. The proposed peer-to-peer system combines our extended algorithms and original dho model. Lock and resource managers operate and interact each other in an architecture based on three levels. Following the experimental study of the underlying system on Grid'5000, and the results obtained, we have proved the performance and stability of the model Dho over a multitude of parameters.
... Update or query operation for location information of a mobile node is performed by a fuzzy logic based 4-group quorum system in a proposed mobility management method [8]. GQS can be constructed from the unfolded surface quorum system with home regions in a wireless mobile Ad-Hoc network as shown in Figure 2. ...
Mobile Ad-Hoc network (MANET) is the network of mobile nodes, which has no fixed infrastructure, and mobile nodes can roam and communicate freely each other. Recently, many researches for mobility management are carried out actively by using location information of nodes. The mobility management is an important issue in MANET because location information of mobile nodes is frequently changed and it aggravates the performance in MANET severely. In this paper, we propose a mobility management method using fuzzy-logic based 4-group quorum system (GQS) by considering the mobile nodes' locality in order to manage location information of mobile nodes in MANET efficiently. The proposed scheme selects mobility databases adaptively from 4-GQS by considering the locality of a mobile node. The performance of the proposed scheme is evaluated by an analytical model and compared with that of existing Uniform Quorum System (UQS) based mobility management scheme.
Coterie is a collection of sets called quorum which satisfies that any two sets have a non-empty intersection and are not property contained in one another. Based on topology, there are many types of coterie, for example, majority coterie. The majority coterie is a type of coterie with more availability than others to solve the problem of a distributed system. There are two types of majority coterie, dominated and non-dominated. The coterie join algorithm is an easy way to construct a new coterie with sizes larger quorum. In this study, we define a union operation for a majority coterie, called a cross-union operation. Then we prove that by using this algorithm, a new coterie is non-dominated if and only if the initial coteries are non-dominated.
We consider the problem of constructing regular group quorum systems of large degree. In particular, we show that for every integer p > 1, there is a regular m-group quorum system over an -element set of degree for every m ≤ p, where each quorum has size p.
The group mutual exclusion problem is a generalization of the ordinary mutual exclusion problem where each application process can be a member of different groups and members of the same group are allowed simultaneous access to their critical sections. Members of different groups must access their critical sections in a mutually exclusive manner. In 2003, Joung proposed a especially designed group quorum system for group mutual exclusion named the surficial system. Given the total number of manager processes in the system n and the number of groups sought m, the degree of the surficial system is , which means that up to k processes can be in their critical section simultaneously. In this paper, we propose a new group quorum system for group mutual exclusion of degree , which is much higher than k. Also, when k= k′, our system produces quorums of smaller size. This makes our system far more efficient and practical.
The (m,h,k)-resource allocation is a conflict resolution problem to control and synchronize a distributed system consisting of n nodes and m shared resources so that the following two requirements are satisfied: at any given time at most h (out of m) resources can be used by some nodes simultaneously, and each resource is used by at most k concurrent nodes. The problem is a natural generalization of several well-studied conflict resolution problems such as mutual
exclusion, k-mutual exclusion, generalized mutual exclusion and group mutual exclusion. The problem can be solved by employing an ℓ-mutual
exclusion algorithm, however, it is inefficient in terms of the message complexity and the maximum degree hk of concurrency may not be achieved. We thus propose a new algorithm and a new quorum system (m, h, k)-coterie used in it, and show that all requirements of the problem are guaranteed and the maximum concurrency degree is achieved
as desired. We also present a natural extension of the new quorum system which resolves a more general problem with distinct
bounded capacities and also achieves the maximum degree of concurrency, åhi=1ki\sum^{h}_{i=1}{k}_{i}, of the problem.
We present a problem, called (n, m, k, d)-resource allocation, to model allocation of group resources with bounded capacity. Specifically, the problem concerns the scheduling of k identical resources among n processes which belong to m groups. Each resource can be used by at most d processes of the same group at a time, but no two processes of different groups can use a resource simultaneously. The problem
captures two fundamental types of conflicts in mutual exclusion: k-exclusion’s amount constraint on the number of processes that can share a resource, and group mutual exclusion’s type constraint on the class of processes that can share a resource. We then study the problem in the message passing paradigm, and investigate
quorum systems for the problem. We begin by establishing some basic and general results for quorum systems for the case of
k = 1, based on which quorum systems for the general case can be understood and constructed. We found that the study of quorum
systems for (n, m, 1, d)-resource allocation is related to some classical problems in combinatorics and in finite projective geometries. By applying
the results there, we are able to obtain some optimal/near-optimal quorum systems.
A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the
area of distributed systems, including mutual exclusion, data replication and dissemination of information. In this paper
we introduce a general class of quorum systems called Crumbling Walls and study its properties. The elements (processors) of a wall are logically arranged in rows of varying widths. A quorum in a wall is the union of one full row and a representative from every row below the full row. This class considerably
generalizes a number of known quorum system constructions. The best crumbling wall is the CWlog quorum system. It has small
quorums, of size O(lg n), and structural simplicity. The CWlog has optimal availability and optimal load among systems with such small quorum size.
It manifests its high quality for all universe sizes, so it is a good choice not only for systems with thousands or millions of processors but also for systems
with as few as 3 or 5 processors. Moreover, our analysis shows that the availability will increase and the load will decrease
at the optimal rates as the system increases in size.
We propose a group mutual exclusion algorithm for unidirectional rings. Our algorithm does not require the processes to have any id. Moreover, processes maintain no special data structures to implement any queues. The space requirement of processes depends only on the number of shared resources, and is equal to 4×log(m+1)+2 bits. The size of messages is 2×log(m+1) bits only. Every resource request generates O(n2) messages in the worst case, but zero messages in the best case
Upper and lower bounds are proved for the shared space requirements for solution of several problems involving resource allocation among asynchronous processes. Controlling the degradation of performance when a limited number of processes fail is of particular interest.
This paper presents a new solution to the group mutual exclusion
problem recently posed by Joung. In this problem, processes repeatedly
request access to various “sessions.” It is required that
distinct processes are not in different sessions concurrently, that
multiple processes may be in the same session concurrently, and that
each process that tries to enter a session is eventually able to do so.
This problem is a generalization of the mutual exclusion and
readers-writers problems. Our algorithm and its correctness proof are
substantially simpler than Joung's. This simplicity is achieved by
building upon known solutions to the more specific mutual exclusion
problem. Our algorithm also has various advantages over Joung's,
depending on the choice of mutual exclusion algorithm used. These
advantages include admitting a process to its session in constant time
in the absence of contention, spinning locally in Cache Coherent (CC)
and Nonuniform Memory Access (NUMA) systems, and improvements in the
complexity measures proposed by Joung
Given a set of nodes in a distributed system, a coterie is a
collection of subsets of the set of nodes such that any two subsets have
a nonempty intersection and are not properly contained in one another. A
subset of nodes in a coterie is called a quorum. An algorithm, called
the join algorithm, which takes nonempty coteries as input, and returns
a new, larger coterie called a composite coterie is introduced. It is
proved that a composite coterie is nondominated if and only if the input
coteries are nondominated. Using the algorithm, dominated or
nondominated coteries may be easily constructed for a large number of
nodes. An efficient method for determining whether a given set of nodes
contains a quorum of a composite coterie is presented. As an example,
tree coteries are generalized using the join algorithm, and it is proved
that tree coteries are nondominated. It is shown that the join algorithm
may be used to generate read and write quorums which may be used by a
replica control protocol
. A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication and dissemination of information Given a strategy to pick quorums, the load L(S) is the minimal access probability of the busiest element, minimizing over the strategies. The capacity Cap(S) is the highest quorum accesses rate that S can handle, so Cap(S) = 1=L(S). The availability of a quorum system S is the probability that at least one quorum survives, assuming that each element fails independently with probability p. A tradeoff between L(S) and the availability of S is shown. We present four novel constructions of quorum system, all featuring optimal or near optimal load, and high availability. The best construction, based on paths in a grid, has a load of O(1= p n), and a failure probability of exp(GammaOmegaGamma p n)) when the elements fail with probability p...
Replicated services accessed via quorums enable each access to be performed at only a subset (quorum) of the servers and achieve consistency across accesses by requiring any two quorums to intersect. Recently, b-masking quorum systems, whose intersections contain at least 2b+1 servers, have been proposed to construct replicated services tolerant of b-arbitrary (Byzantine) server failures. In this paper we consider a hybrid fault model allowing benign failures in addition to the Byzantine ones. We present four novel constructions for b-masking quorum systems in this model, each of which has optimal load (the probability of access of the busiest server) or optimal availability (probability of some quorum surviving failures). To show optimality we also prove lower bounds on the load and availability of any b-masking quorum system in this model.
Abstract. Mutual exclusion and concurrency are two fundamental and essentially opposite features in distributed systems. However, in
some applications such as Computer Supported Cooperative Work (CSCW) we have found it necessary to impose mutual exclusion
on different groups of processes in accessing a resource, while allowing processes of the same group to share the resource.
To our knowledge, no such design issue has been previously raised in the literature. In this paper we address this issue by
presenting a new problem, called Congenial Talking Philosophers, to model group mutual exclusion. We also propose several criteria to evaluate solutions of the problem and to measure their
performance. Finally, we provide an efficient and highly concurrent distributed algorithm for the problem in a shared-memory
model where processes communicate by reading from and writing to shared variables. The distributed algorithm meets the proposed
criteria, and has performance similar to some naive but centralized solutions to the problem.
The design issues for asynchronous group mutual exclusion have been modeled as the Congenial Talking Philosophers, and solutions
for shared-memory models have been proposed [4]. This paper presents an efficient and highly concurrent distributed algorithm
for computer networks where processes communicate by message passing.
In this paper, we propose a simple scheme to construct k-coteries for the distributed k-mutual exclusion problem. The constructed k-coteries are uniform: each quorum in a k-coterie has the same size, O(√N), where N denotes the number of sites in the system.
Group mutual exclusion is a natural problem, formulated by Joung in 1998, that generalises the classical mutual exclusion problem. In group mutual exclusion a process requests a “session” before entering its critical section; processes are allowed to be in the critical section simultaneously provided they have requested the same session. To rule out solutions that cause processes to delay each other even when they all request the same session, group mutual exclusion algorithms must satisfy a property called “concurrent entering”. Joung stated this property only informally. Keane and Moir later gave a precise statement of this property and devised a simple group mutual exclusion algorithm that satisfies it.We argue that Keane and Moir's formulation is not quite as strong as the property Joung described informally. We propose a new precise and simple formulation of concurrent entering that is stronger than Keane and Moir's and properly captures Joung's intention. Keane and Moir's algorithm does not satisfy this stronger property, while Joung's original algorithm does. We present another algorithm that satisfies this stronger property and has some advantages over Joung's.
A network partition can break a distributed computing system into groups of isolated nodes. When this occurs, a mutual exclusion mechanism may be required to ensure that isolated groups do not concurrently perform conflicting operations. We study and formalize these mechanisms in three basic scenarios: where there is a single conflicting type of action; where there are two conflicting types, but operations of the same type do not conflict; and where there are two conflicting types, but operations of one type do not conflict among themselves. For each scenario, we present applications that require mutual exclusion (e.g., name servers, termination protocols, concurrency control). In each case, we also present mutual exclusion mechanisms that are more general and that may provide higher reliability than the voting mechanisms that have been proposed as solutions to this problem.
An algorithm is presented that uses only c√N messages to create mutual exclusion in a computernetwork, where N is the number of nodes and c a constant between 3 and 5. The algorithm issymmetric and allows fully parallel operation.
Quorum-based mutual exclusion algorithms are resilient to node and communication line failures. In order to enter its critical section, a node must obtain permission from a quorum of nodes. A collection of quorums is called a coterie. The most resilient coteries are called nondominated coteries.Recently, k-coteries were proposed to be used in mutual exclusion algorithms that can be used to control access to k identical resources. This article identifies two important classes of k-coteries, proper k-coteries, and nondominated k-coteries. Both classes are important to enhance performance and reliability. Then, several methods are proposed to construct k-coteries that are both proper and nondominated. These methods include weighted voting and composition. Finally, the article presents an important, practical application that controls access to k floating software licenses in a distributed system.
A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication, and dissemination of information. In this paper we study the failure probabilities of quorum systems and in particular of nondominated coteries (NDC). We characterize NDC′s in terms of the failure probability, and prove that any NDC has availability that falls between that of a singleton and a majority consensus. We show conditions for weighted voting schemes to provide asymptotically high availability, and we analyze the availability of several other known quorum systems.
In a distributed system, one strategy for achieving mutual exclusion of groups of nodes without communication is to assign to each node a number of votes. Only a group with a majority of votes can execute the critical operations, and mutual exclusion is achieved because at any given time there is at most one such group. A second strategy, which appears to be similar to votes, is to define a priori a set of groups that intersect each other. Any group of nodes that finds itself in this set can perform the restricted operations. In this paper, both of these strategies are studied in detail and it is shown that they are not equivalent in general (although they are in some cases). In doing so, a number of other interesting properties are proved. These properties will be of use to a system designer who is selecting a vote assignment or a set of groups for a specific application.
The design issues for group mutual exclusion have been modeled by Joung as theCongenial Talking Philoso- phers, and solutions for shared-memory models and com- plete message-passing networks have been proposed (2, 3). These solutions, however, cannot be straightforwardly and efficiently converted to ring networks where each philoso- pher can only communicate directly with its two neighbor- ing philosophers. As rings are also a popular network topology, in this paper we focus the Congenial Talking Philosophers on ring networks and present an efficient and highly concurrent distributed algorithm for the problem.
We propose a quorum system, which we referred to as the surficial quorum system, for group mutual exclusion. The surficial quorum system is geometrically evident and so is easy to construct. It also has a nice structure based on which a truly distributed algorithm for group mutual exclusion can be obtained, and processes’ loads can be minimized. When used with Maekawa’s algorithm, the surficial quorum system allows up to \(
\sqrt {\frac{{2n}}
{{m\left( {m - 1} \right)}}}
\) processes to access a resource simultaneously, where n is the total number of processes, and m is the total number of groups. We also present two modifications of Maekawa’s algorithm so that the number of processes that can access a resource at a time is not limited to the structure of the underlying quorum system, but to the number that the problem definition allows.
The distributed k -mutual-exclusion problem (k-mutex
problem) is the problem of guaranteeing that at most k
processes at a time can enter a critical section at a time in a
distribution system. A method proposed for the solution of the
distributed mutual exclusion problem (i.e., 1-mutex problem) by D.
Barbara and H. Garcia-Molina (1987) is an extension of majority
consensus and uses coteries. The goodness of coterie-based 1-mutex
algorithm strongly depends on the availability of coterie, and it has
been shown that majority coterie is optimal in this sense, provided
that: the network topology is a complete graph, the links never fail,
and p , the reliability of the process, is at least 1/2. The
concept of a k -coterie, an extension of a coterie, is
introduced for solving the k -mutex problem, and lower and upper
bounds are derived on the reliability p for k -majority
coterie, a natural extension of majority coterie, to be optimal, under
conditions (1)-(3). For example, when k =3, p must be
greater than 0.994 for k -majority coterie to be optimal