Switch-matrix architecture and routing for FPDs

An FPD switch module M with w terminals on each side is said to be universal if every set of nets satisfying the dimensional constraint (i.e., the number of nets on each side of M is at most w) is simultaneously routable through M. Chang, Wong, and Wong have identified a class of universal switch blocks. In this paper, we consider the design and routing problems for another popular model of switch modules called switch matrices. Unlike switch blocks, we prove that there exist no universal switch matrices. Nevertheless, we present quasi-universal switch matrices which have the maximum possible routing capacities among all switch matrices of the same size, and show that their routing capacities converge to those of universal switch blocks. Each of the quasi-universal switch matrices of size w has a total of only 14 w - 20 (14 w - 21) switches if w is even (odd), w>1, compared to a fully populated one which has 3 w2-2 w switches. We prove that no switch matrix with less than 14 w - 20 (14 w - 21) switches can be quasi-universal. Experimental results demonstrate that the quasi-universal switch matrices improve routability at the chip level.