Coterie Join Operation and Tree Structured k-Coteries

The coterie join operation proposed by Neilsen and Mizuno produces, from a k-coterie and a coterie, a new k-coterie. For the coterie join operation, this paper first shows 1) a necessary and sufficient condition to produce a nondominated k-coterie (more accurately, a nondominated k-semicoterie satisfying Nonintersection Property) and 2) a sufficient condition to produce a k-conterie with higher availability. By recursively applying the coterie join operation in such a way that the above conditions hold, we define nondominated k-coteries, called tree structured k-coteries, the availabilities of which are thus expected to be very high. This paper then proposes a new k-mutual exclusion algorithm that effectively uses a tree structured k-coterie, by extending Agrawal and El Abbadi's tree algoriyhm. The number of messages necessary for k processes obeying the algorithm to simultaneously enter the critical section is approximately bounded by k log (n / k) in the best case, where n is the number of processes in the system

KETERSEDIAAN OPERASI JOIN DIPERLUAS KOTERI-k TAK-TERDOMINASI

Penelitian ini bertujuan menganalisis ketersediaan dari koteri-  mayoritas tak-terdominasi yang menggunakan operasi join diperluas yaitu penggabungkan koteri- ,  dan  masing-masing atas semesta  dan  dengan unsur tereliminasi , dimana  yang menghasilakan koteri-  tak-terdominasi  atas semesta . Metode penggabungan koteri-  mayoritas tak-terdominasi yang menggunakan operasi join diperluas menghasilkan koteri  atas . Hasil ketersediaan dari operasi join kemudian dibandingkan dengan ketersedian dengan menggunakan operasi join. Dari penelitian ini, menunjukkan bahwa ketersedian operasi join memberikan hasil yang lebih baik jika dibandingkan dengan ketersedian dari operasi join

OPERASI JOIN KOTERI-k DIPERLUAS

Sebagaiman diketahui bahwa koteri-k merupakan perluasan dari definisi koteri yang dapat diterapkan masalah mutex-k. Pada mutex-k terdapat sebanyak k proses yang dapat mengakses sumber daya. Selain itu, kita juga mengenal koteri-k khusus yang disebut dengan koteri-k mayoritas dimana untuk setiap korumnya memiliki ukuran yang sama yang ditentukan dengan . Terdapat beberapa cara dalam penggabungan koter-ki salah satu diantaranya dan sudah tidak asing lagi yaitu operasi join yang merupakan suatu operasi yang digunakan dalam menggabungkan koteri-k mayoritas yang diperkenalkan oleh Neilsen dan Mizuno. Pada operasi join, terdapat salah satu sifat yang menyatakan bahwa jika  dan  tak-terdominasi maka  tak-terdominasi. Ternyata sifat tersebut tidak selamanya berlaku sehingga mengakibatkan koteri-k yang dihasilkan dari operasi join menjadi terdominasi.Tujuan dari penelitian ini yaitu memperkenalkan suatu cara baru dalam menggabungkan koteri-k mayoritas tak-terdominasi yang disebut dengan operasi join diperluas. Dimana operasi join diperluas ini adalah suatu operasi yang dikembangkan dari operasi join yang dibangun dengan cara menggabungkan dua koteri-k mayoritas  dan  yang memiliki ukuran korum yang sama masing-masing atas semesta tak-kosong  dan  dengan unsur tereliminasi , dimana  untuk membentuk  atas semesta tak-kosong . Hasil dari penelitian ini menunjukan bahwa untuk penggabungan dua koteri-k mayoritas tak-terdominasi dengan mengguankan operasi join diperluas akan selalu menghasilkan koteri-k tak-terdominasi dengan nilai k sebelum dan setelah dilakukan operasi penggabungan tidak mengalami perubahan

k-coteries for tolerating network 2-Partition

Network partition, which makes it impossible for some pairs of precesses to communicate with each other, is one of the most serious network failures. Although the notion of k-coterie is introduced to design a k-mutual exclusion algorithm robust against network failures, the number of processes allowed to simultaneously access the critical section may fatally decrease once network partition occurs. This paper discusses how to construct a k-coterie such that the k-mutual exclusion algorithm adopting it is robust against network 2-partition. To this end, we introduce the notion of complemental k-coterie, and show that complemental k-coteries meet our purpose. We then give methods for constructing complemental k-coteries, and show a necessary and sufficient condition for a k-coteries to be complemental

A Union Operation of Non-Dominated K-Coterie in Distributed System

Coterie is a set of quorums which has non-empty intersections and are not part of other quorum. The natural development of the coterie system is k-coterie. The k-coterie consists of 2 types, that are non-dominated k-coterie and dominated k-coterie. The non-dominated k-coterie is more resilient to failure than the dominated k-coterie. Combining two non-dominated k-coterie by applying union operation can result  the dominated k-coterie. This study aims to define a combination of the non-dominated k-coterie with non-dominated k-coterie  using the expanded union operation. The merger of non-dominated k-coterie with the non-dominated k-coterie produces a non-dominated k-coterie

Improving the availability of mutual exclusion Systems on Incomplete Networks

We model a distributed system by a graph G=(V, E), where V represents the set of processes and E the set of bidirectional communication links between two processes. G may not be complete. A popular (distributed) mutual exclusion algorithm on G uses a coterie C(⊆2v), which is a nonempty set of nonempty subsets of V (called quorums) such that, for any two quorums P, Q ∈ C, 1) P∩Q ≠φ and 2) P￠Q hold. The availability is the probability that the algorithm tolerates process and/or link failures, given the probabilities that a process and a link, respectively, are operational. The availability depends on the coterie used in the algorithm. This paper proposes a method to improve the availability by transforming a given coterie

Transversal Merge Operation : A Nondominated Coterie Construction method for distributed mutual exclusion

A coterie is a set of subsets (called quorums) of the processes in a distributed system such that any two quorums intersect with each other and is mainly used to solve the mutual exclusion problem in a quorum-based algorithm. The choice of a coterie sensitively affects the performance of the algorithm and it is known that nondominated (ND) coteries achieve good performance in terms of criteria such as availability and load. On the other hand, grid coteries have some other attractive features : 1) A quorum size is small, which implies a low message complexity, and 2) a quorum is constructible on the fly, which benefits a low space complexity. However, they are not ND coteries unfortunately. To construct ND coteries having the favorite features of grid coteries, we introduce the transversal merge operation that transforms a dominated coterie into an ND coterie and apply it to grid coteries. We call the constructed ND coteries ND grid coteries. These ND grid coteries have availability higher than the original ones, inheriting the above desirable features from them. To demonstrate this fact, we then investigate their quorum size, load, and availability, and propose a dynamic quorum construction algorithm for an ND grid coterie