Quorum based protocols are formalized in terms of data structures called "quorum structures." Several attempts have been made to obtain optimal quorum structures in terms of various measures, such as availability and quorum size. However, the number of quorums under a set of nodes U may be exponential in ?U!, and many essential computations on quorum structures, such as availability analysis, become intractable as the number of nodes becomes large. Thus, obtaining "optimal" quorums under a large set of nodes is extremely difficult. This research will investigate transformations of quorum structures which take quorum structures as input and return new quorum structures. In particular, transformations will be defined which: 1. generate a new structure under a substantially larger set of nodes than the input quorum structures, and 2. preserve certain desirable properties of the input structures, or convert input structures into a structure with desirable properties. Such transformations are extremely useful to generate "good" quorum structures under a large set of nodes for the following reasons: 1. quorum structures which have certain desirable properties may be easily constructed even under a large set of nodes, and 2. a divide and conquer approach may be used for computations on the quorum structures constructed by such transformations. This enables such computations as availability analysis which are otherwise "intractable."
