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Issue No.10 - October (1999 vol.48)
pp: 1107-1122
ABSTRACT
<p><b>Abstract</b>—An FPD switch module <tmath>$M$</tmath> with <tmath>$w$</tmath> terminals on each side is said to be <it>universal</it> if every set of nets satisfying the dimension constraint (i.e., the number of nets on each side of <tmath>$M$</tmath> is at most <tmath>$w$</tmath>) is simultaneously routable through <tmath>$M$</tmath> [<ref type="bib" rid="bibT11078">8</ref>]. Chang et al. have identified a class of universal switch <it>blocks</it> in [<ref type="bib" rid="bibT11078">8</ref>]. In this paper, we consider the design and routing problems for another popular model of switch modules called <it>switch matrices</it>. Unlike switch <it>blocks</it>, we prove that there exist no universal switch <it>matrices</it>. Nevertheless, we present <it>quasi-universal</it> 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 <tmath>$w$</tmath> has a total of only <tmath>$14w-20$</tmath> (<tmath>$14w-21$</tmath>) switches if <tmath>$w$</tmath> is even (odd), <tmath>$w>1$</tmath>, compared to a fully populated one which has <tmath>$3w^2-2w$</tmath> switches. We prove that no switch matrix with less than <tmath>$14w-20$</tmath> (<tmath>$14w-21$</tmath>) switches can be quasi-universal. Experimental results demonstrate that the quasi-universal switch matrices improve routabilty at the chip level.</p>
INDEX TERMS
Analysis, architecture, design, digital, gate array, programmable logic array.
CITATION
Guang-Ming Wu, Yao-Wen Chang, "Quasi-Universal Switch Matrices for FPD Design", IEEE Transactions on Computers, vol.48, no. 10, pp. 1107-1122, October 1999, doi:10.1109/12.805159
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