### Abstract

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-coterie 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 algorithm. The number of messages necessary for k processes obeying the algorithm to simultaneously enter the critical section is approximately bounded by klog(n/k) in the best case, where n is the number of processes in the system.

Original language | English |
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Pages (from-to) | 865-874 |

Number of pages | 10 |

Journal | IEEE Transactions on Parallel and Distributed Systems |

Volume | 12 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 2001 |

### All Science Journal Classification (ASJC) codes

- Signal Processing
- Hardware and Architecture
- Computational Theory and Mathematics

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## Cite this

*IEEE Transactions on Parallel and Distributed Systems*,

*12*(9), 865-874. https://doi.org/10.1109/71.954617