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On Optimum Switch Box Designs for 2-D FPGAs

Each in is referred to as a net of the global routing

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Unformatted text preview: e graph with vertex set and edge set . We denote by (or ) and the number of vertices and edges in , respectively. Let . denotes the induced subgraph of by . We use to denote the path with consecutive vertices . Let and be positive integers with . In [8], we have rep-global routing as a collection resented a of non-empty subsets of such that each elebelongs to exactly subsets of . is ment of called the density of the global routing, and a -global routing is also called a -way global routing with density . Each in is referred to as a net of the global routing. We note that a global routing is a multiple set; two equal sets in represent two different nets in the global routing. Note also that a net of cardinality corresponds to an -pin net. For simplicity, -pin nets are allowed to ensure that each element of appears exactly subsets of . and be global routings and a positive integer. Let and as multiple set is denoted by The union of , and is the union of ’s. Having given a global routing a local and mathematical view, we further view the track with ID on the -th side of an S-box as a vertex and a switc...
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