Use of quorum sets and cyclic quorum sets have proved to be a very useful method to achieve efficient initial data placement and data communication in distributed computation and communication systems. For example, in all-pairs data interaction problems, cyclic quorum sets can be used to avoid communication completely after initial data placement. Searching for all possible cyclic quorum sets for a given number of objects, P, is a task that requires massive computations. This is known to be a hard problem and no time complexity reduction method has been found thus far. In this paper, we try to optimize the search process by avoiding the search space where it is not possible to find a feasible cyclic quorum base set. By studying all possible cyclic quorum sets for given P, we develop insight into the properties of all quorum sets that helps us to reduce the total number of computations significantly compared to that adopting the naïve exhaustive search. We notice that as P grows, better performance could be achieved.