Design of minimum and uniform bipartites for optimum connection blocks of FPGA

The design of optimum connection blocks of field programmable gate arrays (FPGA´s) in number and in distribution of switches is formulated as a bipartite graph design problem and solved. A bipartite with vertex sets R and L (|R|⩽|L|) is called totally perfect if there is a perfect matching from L_s to R for any L_s⊂L with |L_s|⩽|R|. The difference of maximum and minimum degrees of the vertices in L or R is called the skew of the respective vertex set. The problem is to construct a minimum totally perfect bipartite graph with the minimum skew. The result shows that a method, biscattering, can construct such a matrix in O(|R|×|L|) time where the lower bound is attained for both skews. This construction also solves the problem of designing optimum direct-concentrators