We present an efficient optimal algorithm that allocates and schedules cyclic synchronous tasks into fully connected processors. We consider applications with cyclic synchronous tasks with heavy communication traffic, which run on multiprocessors with fully connected communication network. We suggest the computing period as the performance measure to minimize the overall computation time. We use individual start policy for task scheduling, and also introduce concepts and characteristics of the local period and the global period. To solve the complicated optimal scheduling problem in an efficient way, we propose a new spatial scheduling technique using scheduling space which represents all possible schedules in multi-dimensional space. By using spatial searching and enhanced branch-and-bound technique, the optimal task allocation and schedule which minimizes the computing period can be found efficiently. Various examples and scheduling results show the efficiency of the proposed algorithm.