On multicast rearrangeable 3-stage Clos networks without first-stage fan-out

Abstract

For the multicast rearrangeable 3-stage Clos networks where input crossbars do not have fan-out capability, Kirkpatrick, Klawe, and Pippenger gave a sufficient condition and also a necessary condition which differs from the sufficient condition by a factor of 2. In this paper, we first tighten their conditions. Then we propose a new necessary condition based on the a. ne plane such that the necessary condition matches the sufficient condition for an infinite class of 3-stage Clos networks.