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

T. Harada and M. Yamashita, "Coterie Join Operation and Tree Structured k-Coteries," in IEEE Transactions on Parallel & Distributed Systems, vol. 12, no. , pp. 865-874, 2001.
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