Neural Network Parallel Computing for BIBD Problems

Neural network parallel computing for balanced incomplete block design (BIBD) problems is presented in this paper. A design in which all the blocks contain the same number of varieties, and all the varieties occur in the same number of blocks, is called a block design. A block is said to be incomplete if it does not contain all the varieties. If a design is balanced, we call it a balanced incomplete block design. BIBD problems are very important for solving problems in experimental design, material relating design, and coding theory. Two methods for BIBD problems have been proposed. One uses the notion of the finite fields, and the other uses the notion of the difference sets. In general, the conventional algorithms are only able to solve the problems that satisfy an affine plane or a finite projective plane. The proposed algorithm is able to solve BIBD problems regardless of the condition of an affine plane or a finite projective plane. The proposed algorithm requires [formula ommitted] processing elements, or artificial neurons to solve the [k, 1; v]-design problem in parallel. The proposed algorithm was verified by a large number of simulation runs. The simulation results demonstrated that the number of iteration steps for the system to converge to the solution increases slightly with the problem size.