# Distributed k-mutual exclusion problem and k-coteries

## Abstract

The distributed *k*-mutual exclusion problem is the problem of guaranteeing that at most *k* processes are in a critical section simultaneously. This problem can be solved using the *k*-coterie: We first prepare a set (*k*-coterie) *C* of sets (quorums) *Q* of processes such that each *k*-set {*Q*_{1},⋯, *Q*_{k}} of quorums in *C* contains a pair *Q*_{i} and *Q*_{j (i≠j)} intersecting each other. A process wishing to enter a critical section is required to collect a permission from each member of a quorum in *C*. Then at most *k* processes can be in a critical section because of the intersection property of *k*-coterie, and the (average) number of messages necessary for entering a critical section is in proportion to the (average) quorum size of *C*.

This paper proposes a new scheme for constructing a *k*-coterie with small quorums; the size of each quorum is *O*((1/ε)*n*(^{1+3ε})/2) when *k*=*n*^{ε}(0<ε<1/3) and \(O\left( {\sqrt n \log n} \right)\) when *k=O*(1).

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