Combinatorial routing analysis and design of universal switch blocks

A switch block with k sides and W terminals per side ((k,W)-SB) is said to be universal if every set of 2-pin nets satisfying the dimension constraint is simultaneously routable through the switch block. It has been shown that the universal switch blocks (USE) outperform the XC4000-typed switch blocks in routability. In this paper we present a new combinatorial model and routing requirement decomposition theory for analyzing and designing generalized USB models. As a result, we obtain optimum (k,W)-USBs for k/spl les/6 with all Ws, k=7,8 with even Ws; and nearly optimum (k,W)-UBSs for k=7,8 with odd Ws, which is a revised result on the previously published.