(h, k)-arbiters for h-out of-k mutual exclusion problem

h-out of-k mutual exclusion is a generalization of 1-mutual exclusion problem, where there are k limits of shared resources and each process requests h(1⩽h⩽k) units at the same time. Though the k-arbiter has been shown to be a quorum-based solution to this problem, quorums in the k-arbiter are much larger than these in the 1-coterie for 1-mutual exclusion. Thus, the algorithm based on the k-arbiter needs many messages. This paper defines two (h, k)-arbiters for h-out of-k mutual exclusion: a uniform (h, k)-arbiter and a (k+1)-cube (h, k)-arbiter. The quorums in each (h, k)-arbiter are not larger than the ones in the corresponding k-arbiter; consequently using the (h, k)-arbiters is more efficient than using the k-arbiters. Uniform (h, k)-arbiter is an optimal generalization of the majority coterie for 1-mutual exclusion. (k+1)-cube (h, k)-arbiter is a quasi-optimal generalization of square grid coterie for 1-mutual exclusion