Uniform minimal full-access networks

Minimal Full-Access (MFA) networks are the class of all interconnection networks for N = 2ⁿ inputs and outputs that require a minimum number of switching elements and provide full access capability. In this paper, MFA networks with 2 × 2 switching elements that use the same interconnection pattern between the stages are studied; such networks are called uniform MFA (UMFA) networks. Most of the known networks, including the Omega, the binary n-cube, and the regular (2, 2)-banyan, belong to this class. A graph-theoretic approach is used to study the class of UMFA networks, and a procedure is described to derive topologically nonequivalent networks from the Omega network. It is shown that the number of UMFA networks grow exponentially with N, and a lower bound of about 2^N/32 is obtained for N ⩾ 32. We also outline an extension of our methods to derive similar bounds for networks using k × k switches, for k ⩾ 3.