On Optimum Switch Box Designs for 2-D FPGAs

Is called a detailed routing of a hyper universal

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Unformatted text preview: h connecting the track with ID on the -th side and the track with ID on the -th side is an edge . can be represented as a Therefore, any -way S-box of density -partite graph on , where and each is an independent set in for . We call such a graph a -design. In particular, a -way S-box of density is a -design. Let be a -design on . A detailed routing (or shortly detailed routing) of a -global routing in is a set of mutually vertex disjoint subgraphs of satisfying: (1) is a tree of vertices, and (2) if , for . is called a detailed routing of . A hyper-universal -design on is a design on such that it contains a detailed routing for each -global routing. For example, the complete -partite graph on (in which, there is an edge joining each pair of vertices and with ) is a hyper-universal design. A hyper-universal -design represents a -way S-box (also called a S-box) which can accommoof density dates any -global routings. An optimum -design is a hyper-universal -design with the minimum number of edges. Clearly, the number of edges -design is uniqu...
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