Issue No. 07 - July (1993 vol. 4)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.238300
<p>A coterie under a ground set U consists of subsets (called quorums) of U such that anypair of quorums intersect with each other. Nondominated (ND) coteries are of particularinterest, since they are optimal in some sense. By assigning a Boolean variable to eachelement in U, a family of subsets of U is represented by a Boolean function of thesevariables. The authors characterize the ND coteries as exactly those families which canbe represented by positive, self-dual functions. In this Boolean framework, it is provedthat any function representing an ND coterie can be decomposed into copies of thethree-majority function, and this decomposition is representable as a binary tree. It isalso shown that the class of ND coteries proposed by D. Agrawal and A. El Abbadi (1989) is related to a special case of the above binary decomposition, and that the composition proposed by M.L. Neilsen and M. Mizuno (1992) is closely related to the classical Ashenhurst decomposition of Boolean functions. A number of other results are also obtained. The compactness of the proofs of most of these results indicates the suitability of Boolean algebra for the analysis of coteries.</p>
Index Termscoteries; mutual exclusion; distributed systems; quorums; Boolean variable; Booleanfunction; self-dual functions; three-majority function; binary tree; binary decomposition;classical Ashenhurst decomposition; compactness; Boolean algebra; Boolean functions;distributed processing; tree data structures
T. Ibaraki and T. Kameda, "A Theory of Coteries: Mutual Exclusion in Distributed Systems," in IEEE Transactions on Parallel & Distributed Systems, vol. 4, no. , pp. 779-794, 1993.