Nondominated Research Articles

A new transformation method for nondominated coterie design

Coteries are general schemes for distributed mutual exclusion solutions. Garcia-Molina and Barbara developed a transformation algorithm to transform one nondominated (ND) coterie to another [5]. The algorithm may properly be used to partially enumerate ND coteries. However, the transformation algorithm proposed is not appropriate for the case of large coterie design because properties of the new produced ND coterie are not easily predictable. We introduce a hierarchical transformation concept to provide a simple way to produce new larger ND coteries through transformation from smaller ND coteries. By systematically applying our transformation, coteries can scale well for a large number of nodes. Furthermore, the new generated coteries will inherit the properties of original coteries. This makes the transformation more predictable than trial and error. We also devise a heuristic algorithm to construct hierarchical structures aimed at maximizing availability in the context of heterogeneous systems.

A theory of coteries: mutual exclusion in distributed systems

A coterie under a ground set U consists of subsets (called quorums) of U such that any pair of quorums intersect with each other. Nondominated (ND) coteries are of particular interest, since they are optimal in some sense. By assigning a Boolean variable to each element in U, a family of subsets of U is represented by a Boolean function of these variables. The authors characterize the ND coteries as exactly those families which can be represented by positive, self-dual functions. In this Boolean framework, it is proved that any function representing an ND coterie can be decomposed into copies of the three-majority function, and this decomposition is representable as a binary tree. It is also 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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>