### Abstract

The distributed k-mutual exclusion problem (kmutex problem) is the problem of guaranteeing that at most k processes can enter a critical section at a time in a distributed system. The distributed mutual exclusion problem (i.e., 1-mutex problem) is considered as one of the most fundamental distributed problems and several methods have been proposed for solving it. One of such methods, which is proposed by Barbara and Garcia-Molina as an extension of majority consensus, 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 1) the network topology is a complete graph, 2) the links never fail, and 3) p, the reliability of process, is at least 1/2. This paper introduces the concept of a k-coterie as an extension of a coterie for solving the k-mutex problem, and derives a lower and an upper bounds on the reliability p for k-majority coterie, a natural extension of majority coterie, to be optimal, under the same conditions l)-3). For example, when k = 3, p must be greater than 0.994 for k-majority coterie to be optimal.

Original language | English |
---|---|

Pages (from-to) | 553-558 |

Number of pages | 6 |

Journal | IEEE Transactions on Computers |

Volume | 42 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 1993 |

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### All Science Journal Classification (ASJC) codes

- Software
- Theoretical Computer Science
- Hardware and Architecture
- Computational Theory and Mathematics

### Cite this

*IEEE Transactions on Computers*,

*42*(5), 553-558. https://doi.org/10.1109/12.223674

**Availability of k-Coterie.** / Kakugawa, Hirotsugu; Yamashita, Masafumi; Fujita, Satoshi; Ae, Tadashi.

Research output: Contribution to journal › Article

*IEEE Transactions on Computers*, vol. 42, no. 5, pp. 553-558. https://doi.org/10.1109/12.223674

}

TY - JOUR

T1 - Availability of k-Coterie

AU - Kakugawa, Hirotsugu

AU - Yamashita, Masafumi

AU - Fujita, Satoshi

AU - Ae, Tadashi

PY - 1993/5

Y1 - 1993/5

N2 - The distributed k-mutual exclusion problem (kmutex problem) is the problem of guaranteeing that at most k processes can enter a critical section at a time in a distributed system. The distributed mutual exclusion problem (i.e., 1-mutex problem) is considered as one of the most fundamental distributed problems and several methods have been proposed for solving it. One of such methods, which is proposed by Barbara and Garcia-Molina as an extension of majority consensus, 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 1) the network topology is a complete graph, 2) the links never fail, and 3) p, the reliability of process, is at least 1/2. This paper introduces the concept of a k-coterie as an extension of a coterie for solving the k-mutex problem, and derives a lower and an upper bounds on the reliability p for k-majority coterie, a natural extension of majority coterie, to be optimal, under the same conditions l)-3). For example, when k = 3, p must be greater than 0.994 for k-majority coterie to be optimal.

AB - The distributed k-mutual exclusion problem (kmutex problem) is the problem of guaranteeing that at most k processes can enter a critical section at a time in a distributed system. The distributed mutual exclusion problem (i.e., 1-mutex problem) is considered as one of the most fundamental distributed problems and several methods have been proposed for solving it. One of such methods, which is proposed by Barbara and Garcia-Molina as an extension of majority consensus, 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 1) the network topology is a complete graph, 2) the links never fail, and 3) p, the reliability of process, is at least 1/2. This paper introduces the concept of a k-coterie as an extension of a coterie for solving the k-mutex problem, and derives a lower and an upper bounds on the reliability p for k-majority coterie, a natural extension of majority coterie, to be optimal, under the same conditions l)-3). For example, when k = 3, p must be greater than 0.994 for k-majority coterie to be optimal.

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UR - http://www.scopus.com/inward/citedby.url?scp=0027592888&partnerID=8YFLogxK

U2 - 10.1109/12.223674

DO - 10.1109/12.223674

M3 - Article

AN - SCOPUS:0027592888

VL - 42

SP - 553

EP - 558

JO - IEEE Transactions on Computers

JF - IEEE Transactions on Computers

SN - 0018-9340

IS - 5

ER -