On Optimum Switch Box Designs for 2-D FPGAs

In 8 we have developed a general reduction technique

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Unformatted text preview: 52  f c ¥ H£ E ¥E vH£ , , C ¥ HR  £ ¡ , C ¡ ¥ H£ E , 2  ¨V ¥ , 2 ¥  , , ¥U¥  £  R ¥E SvH£ E ¢ £E E , ©   E , -design for ’s for , , ¤  ¡           E ¥ U¥ H£ E  T HEOREM 5. For design. -design for as the following graph: disjoint union of disjoint union of disjoint union of disjoint union of disjoint union of disjoint union of , , -DESIGN ¥ ¦¥  £ ¡ E , ,  ¥ H£ E I P F E , , ¥ ¦¥  £   is a hyper-universal , ,  £  †" " F £ £ U I ‰ P , , A9 B@ is an optimum By the definition of number of edges of , , ¥¦¥  £  ¥ ¦¥ ¥ ¦¤ ¥ 7    Y W Now define , , ¥ L EMMA 4. We note that we have given an efficient algorithm for IV. Now we focus on -way S-box designs. For Step 1, Lemma 1 shows that . For Step 2, [8] showed that any -global routing can be decomposed as a union of -global routings and at most -global routing for some and . -global routings. The following are all primitive minimal ,  @ ¥ U¥  £ L EMMA 3. IV. Design an efficient detailed routing algorithm...
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